Is Matthew 28 saying something about Baptism?

It seems that there are two distinct things that we are commanded to do to those whom we are making disciples--baptize them and teach them obedience to what God has commanded.

It should be noted that the mark of a disciple is obedience to what God has commanded (in addition to obeying the Lord in baptism). It almost seems that there are two distinct things we ought to be doing in order to make disciples. If we are to disciple someone, we should baptize them and we should teach them obedience to Christ.

It does not seem feasible that the intent is that we make disciples, then baptize them and teach them to obey. A disciple without obedience is not a disciple. By the same token, a disciple without baptism is not a disciple, since that is a basic commandment of God that we are to obey.

So, with regard to baptism and what this verse is teaching about it, it seems that it is part of the discipleship process to be performed in conjunction with the teaching of obedience to Christ.

We would not be able to teach an infant obedience to Christ until perhaps the age of 3 or so. That would not mean we could not baptize them. The bigger issue there is the involuntary nature of an infant's baptism.

UPDATE - I am restructuring my answer to better conform to the OP questions as suggested.

From the OP,

My question here is, is the Great Commission trying to make a doctrinal point about baptism?

No, this verse is not making a "complete" doctrinal statement on Baptism. Although, it does conform and support the doctrine of believers baptism found elsewhere in scripture.

Is there anything being said about baptism, particularly infant baptism?

No. First, this verse isn't sufficient alone to make doctrinal statements about Baptism. Only doctrine you can draw from this verse about baptism is to support more detailed verses on baptism elsewhere. This verse does logically support believers baptism but when compared to other verses, one cannot make the leap from this verse to support infant baptism.

Does the Great Commission support Believer's Baptism since "making disciples" comes first?

Yes. As I have stated above, even if the Greek translates to a seemingly concurrent act, it still mentions "making disciples" first, then baptism, you can be sure of the doctrine by comparing to other scripture.

For example, believer's baptism is shown very clearly in Acts 8:35-38

35 Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus.

36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?

37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.

38 And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.

This is very clear that belief in Christ has to come before baptism. Baptism is a picture of the death, burial, and resurrection of Christ. It is a public profession of the inward change of the believer.

Thus, if the order for baptism in Mathew 28 can be seen and checked from other scripture, then you can easily have your answer to:

What are the doctrinal implications here, if any?

The answer is the verse alone cannot be used to form a complete doctrinal position on baptism but at the same time does not allow for infant baptism but does support believer's baptism.

As some commercial on Relevant Radio always says, if you're baptized, you're a missionary

1270 "Reborn as sons of God, [the baptized] must profess before men the faith they have received from God through the Church" and participate in the apostolic and missionary activity of the People of God.

CCC 1270

So, if an infant is baptized, does that infuse some sort of missionary zeal? No not really , that's what faith formation is for and that's what one professes when one is confirmed and receives the Holy Eucharist. There are three sacraments of initiation, not just one Baptism. There is also a lifetime learning and praying and good works to be done.

But, I have to say, that was an astute and awesome observation you made there. I don't know if it's ever been used as a justification for infant baptism or a test to prove the necessity of post-baptismal confirmation, but both these things exist and they certainly do so in accord with your reading of scripture. Unless the Holy Spirit infused knowledge to the thousand baptized after Pentecost Himself, this has to be the same Baptism Jeaus is talking about. Baptize into discipleship, afterwords the Apostles (who later became the Bishops) would come to seal you with the Holy Spirit like what St. Paul did in Acts 19:4-6 where he baptized followers of John into Christ's baptism and he laid his hands on them as a sin of confirmation, for they were alereadly formed spiritually.

P.S. I know this is an unapologetically Catholic answer and potentially not what you're looking for at all, but I figured I'd put my two cents in as the other answers take for grante that infant baptism is done in error.

The baptizing mentioned in Matthew 28 is not so much as a command as a part of a command. The sentence structure here in the greek has one verb which is 'go'. Everything else modifies how we should go. We should go discipling, we should go baptizing, we should go teaching.

Those commenting on the order of the words are, I believe, correct. The order is not significant. Also note that the 'them' that are to be baptized here refers to the 'nations' that have been discipled. God calls the people who are called by His name to receive the covenant sign of inclusion (baptism in the New Testament circumcision in the Old Testament).

It is true that those who are outside the covenant should convert to the Christian faith before receiving baptism (Acts 8:12) but that still leaves the question about those who grow up in the Christian Faith. Paul clearly states that the children of one believing parent are somehow set aside and different. I believe that the difference here is that the children are part of the covenant community.

Going along with this answer from the other site, I think that saying that this supports "believers' baptism only" is a long stretch grammatically. Rather, the doctrinal point is that the two should be held together. "If you are baptized, then you are a disciple" along with "if you are a disciple, then you are baptized."

As another thought: if it is saying that "believer's baptism is the only way," then that implies that it is possible to be a proper disciple without being baptized. Personally, I see that as a hard sell.