All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is permissible for you to marry this woman and you will be rewarded for doing so if you intend to preserve her chastity and keep yourself chaste from illegal sexual intercourse. The sins which she committed before, like fornication and the like, should not be taken into account if she had repented and embraced Islam, as Islam wipes out the previous sins, and repentance wipes out the previous sins as well. For more benefit, please refer to Fataawa 90666 and 89823.
As regards her child, he should be traced back to his mother as there is no relation between him and the fornicator [his illegal father]. Since the child has no legitimate father, then the fornicator has no religious obligations towards him.
The Prophet said: "The boy is for (i.e traced to) the owner of the bed (legitimate husband) and the stone is for the person who commits an illegal sexual intercourse (i.e. the child will not be traced back to him)." [Al-Bukhari & Muslim].
For more benefit, please refer to Fataawa 92108 and 83071.
Allaah Knows best.