What were women doing at the Battle of Dorylaeum during the First Crusade?

SHORT ANSWERS

The Presence of Noble Ladies: The First Crusade included a large number of pilgrims, many of whom were women (including female relatives of nobles). Concerning their presence at the battle itself, there was no nearby safe refuge when the Turks attacked.

Rape over Death: The church's view was that victims of rape in war did not have to do penance. Also, the account of the 'noble girls' can be reasonably interpreted as them trying to save other prisoners (including children) as well as (possibly or probably) themselves.

DETAILS

In answering your first question, What "delicate and noble" girls were doing in the middle of a battle, we can look back to 1095 at Clermont, the moment that Pope Urban II called for a crusade:

In the weeks and months that followed, the pope's impassioned appeal swept across Europe, prompting some 100,000 men and women, from knight to pauper, to take up the call - the largest mobilisation of manpower since the fall of the Roman Empire....

Source: Thomas S. Asbridge, 'The First Crusade: A New History' (2004)

This wasn't quite what he had intended but he shouldn't have been surprised at the response for:

as a sub-species of pilgrimage, the crusade was a penitential act, and thus both voluntary and open to all Christians. The very feature that had made Urban's message so palatable - its packaging within an existing framework of devotional practice - meant that the principle of unrestricted participation was imported into, and imposed upon, the precepts of crusading, making it all but impossible to control recruitment.

Source: Asbridge

Thus, thousands accompanied the military element as pilgrims, a situation which was to greatly increase the problem of supplies during the crusade. On these non-combatants, the number

was certainly high. A large number of knights brought their ladies with them. Raymond of Toulouse was accompanied by his wife, and Baldwin of Boulogne by his wife and children. Bohemond had at least one sister with him. We know the names of several ladies that took part in Robert of Normandy's expedition; and occasionally other ladies appear in the story. All these ladies brought attendants; and there was certainly a large number of humbler women, respectable and the reverse, with the army.

Source: Steven Runciman, 'A History of the Crusades, Volume 1' (1987) (Note that it is disputed as to whether Baldwin had any children with his wife at this time.)

To pilgrimage, we can probably add (in some cases at least) duty and (in the case of servant women) obligation. Also, many crusaders were younger sons who had no expectation of inheriting land; at least some planned to gain land in the east and settle there, and thus they took their families. This may have been the case with Baldwin, who became king of Jerusalem in 1100.

The fighting men were, of course, the best protection these non-combatants had on their journey to the Holy Land. Consequently, the non-combatants (noble ladies and all) found themselves in the middle of the Battle of Dorylaeum when the Turks attacked as there was no nearby safe refuge: the crusaders were by this time too far from Nicaea (never mind Constantinople) to send the noble ladies there.

On your second question, the noble ladies submitting to rape rather than death, the answer may lie in how one interprets Albert of Aachen's account. From the link provided by sempaiscuba, we can get a fuller version of what Asbridge was referring to:

The Turks, with their prince Suleyman, were growing stronger and stronger, they burst into the camp in strength, striking with arrows from their horn bows, killing pilgrim foot-soldiers, girls, women, infants and old people, sparing no one on grounds of age. Stunned and terrified by the cruelty of this most hideous killing, girls who were delicate and very nobly born were hastening to get themselves dressed up, offering themselves to the Turks so that at least, roused and appeased by love of their beauty, the Turks might learn to pity their prisoners.

Given that the last sentence ends with "pity their prisoners", we could reasonably interpret this to mean that the ladies were attempting to save the lives of the other non-combatants (among whom were children). Alternatively (or perhaps even additionally), they may have seen it as justifiable even just for themselves, that they could be later forgiven and purified.

Interestingly, Albert's history has account of a nun forgiven for submitting herself to rape just a few weeks before the Battle of Dorylaeum (1st July 1097). After Nicaea fell to the Crusaders (18th June 1097), Albert writes

many of the Christians' prisoners were returned, a certain nun from the convent of St Mary at the Granaries...claimed she had been captured ... been taken in a vile and detestable union by a certain Turk and others with scarcely a pause. Then, while she was uttering her wretched moans ... she recognized Henry of the castle of Esch among the nobles and soldiers of Christ. Addressing him by name in a low and tearful voice, she appealed to him to come to the aid of her purification. He recognized her at once, and was affected by her misfortune, and he employed diligence and every argument of pity he could with Duke Godfrey until advice for repetance was given her by Lord Adhemar, the venerable bishop.... she was granted forgiveness for her unlawful liaison with the Turk, and her repentance was made less burdensome because she had endured this hideous defilement by wicked and villainous men under duress and unwillingly.

According to Albert, though, the nun later went back to the Turk but Asbridge casts some doubt on this 'ending'; the Turk, assuming he was still even alive after the fall of Nicaea, would have been a captive.

How a raped woman was regarded at the time depended very much on the circumstances and the male relatives of the victim. There are cases ranging from a raped daughter being put to death to a husband who, accepting his wife's word that she was a victim, challenged her rapist to a duel to the death (the rapist lost). Also, specific examples of medieval rape victims (and potential victims) show that they clearly had different feelings on how they should respond. By and large, though, it seems that rape victims in war (in the eyes of the church at least) had a good chance of not having to do penance; Pope Gregory I (died 604) stated this specifically, and the 9th century Capitula Judiciorum said "that women who had been raped in warfare were free from penance."

Other sources:

Stephen P. Pistono, 'Rape in Medieval Europe'. In 'Atlantis Vol. 14 No. 2' (1989) (link automatically downloads pdf)

Ashley Nicole Wallace, 'Jeopardized Virginity an Analysis of Rape and Spiritual Virginity in Medieval Europe' (thesis, 2015)

The Christian View on Rape

Niels Ebdrup, 'The church changed the perception of rape' (2012)

Belina (virgin)