What happens to unborn, unbaptized babies who die?

"Children that cannot understand sin cannot commit sin. Therefore they do not need baptism and cannot repent of their sins. Therefore unborn children (along with other very young children) gain immediate acceptance into heaven."

I wholeheartedly agree with this viewpoint found above.
Mark 10:14 seems in line with this: "But when Jesus saw it, he was much displeased, and said unto them, Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God."

The official Catholic position, from the CCC, Section 2, Article 1, would seem to be the following sections, in particular item 1261 (and quite similar to the Lutheran position).

The Baptism of infants:

1250 Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called. The sheer gratuitousness of the grace of salvation is particularly manifest in infant Baptism. The Church and the parents would deny a child the priceless grace of becoming a child of God were they not to confer Baptism shortly after birth.

1251 Christian parents will recognize that this practice also accords with their role as nurturers of the life that God has entrusted to them.

1252 The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole “households” received baptism, infants may also have been baptized.

The Necessity of Baptism:

1260 “Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery.” Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.

1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: “Let the children come to me, do not hinder them,” allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy Baptism.

Where the summary would be that the Church hopes (hopes as in the mystical sense, which is a firm hope based on the faithfulness of God) that God has made a way for those who are not baptized at death, but who would have otherwise "desired" baptism.

Complementing Jesus Christ's many words, Exodus 30:14+ also provides a definite hint as to the beginning of the age of self-determination. So, age groups 20 and below are accounted for by God.

If you read Acts 10:43 it says "To him all the prophets witness that, through His name, whoever believes in him will receive remission of sins." So I think an unborn child knows nothing more than the glory of God, and the sacrifice of Jesus Christ. He will be forgiven of any(if any) sin that exists and be accepted as a child of the Lord.

Catholics used to believe that they went to the Limbo of the Children (a part of Hell where there is no fire)

Pope Eugene IV, Council of Florence, “Letentur coeli,” Sess. 6, July 6, 1439, ex cathedra:

We define also that… the souls of those who depart this life in actual mortal sin, or in original sin alone, go straightaway to hell, but to undergo punishments of different kinds.

However Benedict XVI abolished the concept of Limbo, claiming that it was never defined.

One verse I have heard in support of salvation of infants is in 2 Samuel 12:22-23, after King David's young child (not sure how young) dies.

22 He said, “While the child was still alive, I fasted and wept; for I said, ‘Who knows, the LORD may be gracious to me, that the child may live.’ 23 But now he has died; why should I fast? Can I bring him back again? I will go to him, but he will not return to me.”

The idea presented from this is that "I will go to him" indicates that David plans to see his child in heaven.

I realize this doesn't specifically address unborn babies, but I think the same logic would hold.

Babies and children do not know the difference between right and wrong, and the Bible calls them "those who cannot tell between their right hand and their left." (Jonah 4:11)

Because they do not understand what is right, what is wrong, as they are too young, they do not consciously sin. They are innocent. There will come a time when they understand what is right and what is wrong, but until then, they are counted as "saved". God has a provision for babies and very young children who die early.

Edit:

This site puts it better.

Besides, Jesus did state that unless we were like the little children, we wouldn't go to heaven.

This is a topic that is close to the heart of many, and as such, I hope not to offend anyone. I lost a child at 20 weeks, he was a misscarriage, and my wife was able to deliver him naturally. (I am not looking for sympathy). The doctrine of the LDS Church, of which I am part, had great healing and comfort for me. This come from The Book of Mormon, Moroni 8 with select verses below.

5 For, if I have learned the truth, there have been disputations among you concerning the baptism of your little children.

6 And now, my son, I desire that ye should labor diligently, that this gross error should be removed from among you; for, for this intent I have written this epistle.

7 For immediately after I had learned these things of you I inquired of the Lord concerning the matter. And the word of the Lord came to me by the power of the Holy Ghost, saying:

8 Listen to the words of Christ, your Redeemer, your Lord and your God. Behold, I came into the world not to call the righteous but sinners to repentance; the whole need no physician, but they that are sick; wherefore, little children are whole, for they are not capable of committing sin; wherefore the curse of Adam is taken from them in me, that it hath no power over them; and the law of circumcision is done away in me.

11 And their little children need no repentance, neither baptism. Behold, baptism is unto repentance to the fulfilling the commandments unto the remission of sins.

12 But little children are alive in Christ, even from the foundation of the world; if not so, God is a partial God, and also a changeable God, and a respecter to persons; for how many little children have died without baptism!

13 Wherefore, if little children could not be saved without baptism, these must have gone to an endless hell.

14 Behold I say unto you, that he that supposeth that little children need baptism is in the gall of bitterness and in the bonds of iniquity; for he hath neither faith, hope, nor charity; wherefore, should he be cut off while in the thought, he must go down to hell.

15 For awful is the wickedness to suppose that God saveth one child because of baptism, and the other must perish because he hath no baptism.

19 Little children cannot repent; wherefore, it is awful wickedness to deny the pure mercies of God unto them, for they are all alive in him because of his mercy.

20 And he that saith that little children need baptism denieth the mercies of Christ, and setteth at naught the atonement of him and the power of his redemption.

21 Wo unto such, for they are in danger of death, hell, and an endless torment. I speak it boldly; God hath commanded me. Listen unto them and give heed, or they stand against you at the judgment-seat of Christ.

22 For behold that all little children are alive in Christ, and also all they that are without the law. For the power of redemption cometh on all them that have no law; wherefore, he that is not condemned, or he that is under no condemnation, cannot repent; and unto such baptism availeth nothing—

23 But it is mockery before God, denying the mercies of Christ, and the power of his Holy Spirit, and putting trust in dead works.

To summarize, little children are alive in Christ and have no need for repentance, therefore baptism is not necessary for them until they reach the age of accountability. If you have lost a little child, he or she is alive with God and peace should be found. This is how my wife and I were able to find comfort in the loss of our son.

This is the official Catholic position:

On April 22, 2007, the advisory body known as the International Theological Commission released a document, originally commissioned by Pope John Paul II, entitled "The Hope of Salvation for Infants Who Die without Being Baptized."[8] After tracing the history of the various opinions that have been and are held on the eternal fate of unbaptized infants, including that connected with the theory of the Limbo of Infants, and after examining the theological arguments, the document stated its conclusion as follows:

Our conclusion is that the many factors that we have considered above give serious theological and liturgical grounds for hope that unbaptized infants who die will be saved and enjoy the beatific vision. We emphasize that these are reasons for prayerful hope, rather than grounds for sure knowledge. There is much that simply has not been revealed to us. We live by faith and hope in the God of mercy and love who has been revealed to us in Christ, and the Spirit moves us to pray in constant thankfulness and joy.

103 What has been revealed to us is that the ordinary way of salvation is by the sacrament of baptism. None of the above considerations should be taken as qualifying the necessity of baptism or justifying delay in administering the sacrament. Rather, as we want to reaffirm in conclusion, they provide strong grounds for hope that God will save infants when we have not been able to do for them what we would have wished to do, namely, to baptize them into the faith and life of the Church.

Pope Benedict XVI authorized publication of this document, indicating that he considers it consistent with the Church's teaching, though it is not an official expression of that teaching.[32] Media reports that by the document "the Pope closed Limbo"[33] are thus without foundation. In fact, the document explicitly states that "the theory of limbo, understood as a state which includes the souls of infants who die subject to original sin and without baptism, and who, therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin.

More can be found here: Limbo (Wikipedia).

One of the supporting scripture for the salvation requires baptism doctrine is this verse:

Acts 2:38
Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit."

This verse is saying that forgiveness of sins requires repentance and baptism. However, the very foundation is that those are required for the forgiveness of sins.

The essence of this question is this: Are unborn children guilty of sin?

For that, you have to ask What is the essence of sin? To answer that question, sin is the turning away from God's will. It's knowing God's desires for you--his rules if you prefer--and intentionally doing otherwise.

My argument is that these children can not know sin because they cannot know right from wrong.

Summary

Children that cannot understand sin cannot commit sin. Therefore they do not need baptism and cannot repent of their sins. Therefore unborn children (along with other very young children) gain immediate acceptance into heaven.