There is no "best thing" to do in this situation, only things are are relatively more or less morally palatable to the young woman.
I question why you tossed AIDS into the mix in this question. Just to be perfectly correct, no one ever "contracts AIDS". You can catch the HIV virus from unprotected sex, but being HIV positive is not at all the same thing as having AIDS. In the nine-month time frame of your question, the mother's health will most likely not be affected by the virus even if she is HIV-positive. A child will, according to UNICEF, contract the HIV virus from its mother in about 15-25% of cases; the longer the mother has carried the virus the more likely she is to pass it to her child, which means in this case her child's odds of being born HIV-free are very good indeed.
In answer to your question, in the US it's the woman's choice whether or not to terminate her pregnancy. If she chooses to, she should be well-informed before making her decision. Either way, she will have to live with her decision. If she carries the child to term, she has other choices to make; whether to keep it and try to raise it (which raises the question of what happens if she gets sick), or whether to give it up for adoption.
If I were counseling this young woman, I would not presume to tell her what to do, I would try to give her the truth about her various options and encourage her to choose the decision she can best live with.