Objection 1. It seems that a child can be baptized while yet in its mother's womb. For the gift of Christ is more efficacious unto salvation than Adam's sin unto condemnation, as the Apostle says (Romans 5:15). But a child while yet in its mother's womb is under sentence of condemnation on account of Adam's sin. For much more reason, therefore, can it be saved through the gift of Christ, which is bestowed by means of Baptism. Therefore a child can be baptized while yet in its mother's womb.
Objection 2. Further, a child, while yet in its mother's womb, seems to be part of its mother. Now, when the mother is baptized, whatever is in her and part of her, is baptized. Therefore it seems that when the mother is baptized, the child in her womb is baptized.
Objection 3. Further, eternal death is a greater evil than death of the body. But of two evils the less should be chosen. If, therefore, the child in the mother's womb cannot be baptized, it would be better for the mother to be opened, and the child to be taken out by force and baptized, than that the child should be eternally damned through dying without Baptism.
Objection 4. Further, it happens at times that some part of the child comes forth first, as we read in Genesis 38:27: "In the very delivery of the infants, one put forth a hand, whereon the midwife tied a scarlet thread, saying: This shall come forth the first. But he drawing back his hand, the other came forth." Now sometimes in such cases there is danger of death. Therefore it seems that that part should be baptized, while the child is yet in its mother's womb.
On the contrary, Augustine says (Ep. ad Dardan.): "No one can be born a second time unless he be born first." But Baptism is a spiritual regeneration. Therefore no one should be baptized before he is born from the womb.
I answer that, It is essential to Baptism that some part of the body of the person baptized be in some way washed with water, since Baptism is a kind of washing, as stated above (Question 66, Article 1). But an infant's body, before being born from the womb, can nowise be washed with water; unless perchance it be said that the baptismal water, with which the mother's body is washed, reaches the child while yet in its mother's womb. But this is impossible: both because the child's soul, to the sanctification of which Baptism is ordained, is distinct from the soul of the mother; and because the body of the animated infant is already formed, and consequently distinct from the body of the mother. Therefore the Baptism which the mother receives does not overflow on to the child which is in her womb. Hence Augustine says (Cont. Julian. vi): "If what is conceived within a mother belonged to her body, so as to be considered a part thereof, we should not baptize an infant whose mother, through danger of death, was baptized while she bore it in her womb. Since, then, it," i.e. the infant, "is baptized, it certainly did not belong to the mother's body while it was in the womb." It follows, therefore, that a child can nowise be baptized while in its mother's womb.
Reply to Objection 1. Children while in the mother's womb have not yet come forth into the world to live among other men. Consequently they cannot be subject to the action of man, so as to receive the sacrament, at the hands of man, unto salvation. They can, however, be subject to the action of God, in Whose sight they live, so as, by a kind of privilege, to receive the grace of sanctification; as was the case with those who were sanctified in the womb.
Reply to Objection 2. An internal member of the mother is something of hers by continuity and material union of the part with the whole: whereas a child while in its mother's womb is something of hers through being joined with, and yet distinct from her. Wherefore there is no comparison.
Reply to Objection 3. We should "not do evil that there may come good" (Romans 3:8). Therefore it is wrong to kill a mother that her child may be baptized. If, however, the mother die while the child lives yet in her womb, she should be opened that the child may be baptized.
Reply to Objection 4. Unless death be imminent, we should wait until the child has entirely come forth from the womb before baptizing it. If, however, the head, wherein the senses are rooted, appear first, it should be baptized, in cases of danger: nor should it be baptized again, if perfect birth should ensue. And seemingly the same should be done in cases of danger no matter what part of the body appear first. But as none of the exterior parts of the body belong to its integrity in the same degree as the head, some hold that since the matter is doubtful, whenever any other part of the body has been baptized, the child, when perfect birth has taken place, should be baptized with the form: "If thou art not baptized, I baptize thee," etc.
Source: Summa Theologica (New Advent)