Answer

First, for a summary of the opinions and the relevant Jewish law, see here:
https://www.yeshiva.org.il/midrash/458 
I am inclined to say that an abortion should not be performed in such a case (especially if the abortion would be done after three months of pregnancy; see the link above). Rabbi Melamed also writes that according to all halakhic decisors this is forbidden if the motive is like ours here (see there regarding pregnancy outside marriage, not rape). The young woman and her partner need to bear the consequences of their actions, and it is hard to accept permission to kill in order not to bear consequences for which they are responsible. If she cannot raise the child, she can give him or her up for adoption. If she does not want that either, then it is absurd to tell her to abort so that she will not have to place the child for adoption. After all, killing him or her is certainly not preferable to the child not being raised by his or her biological mother.
As I told you, in my view the moral prohibition is more severe than the halakhic one. In Jewish law there might perhaps have been room to be lenient.
A halakhic decisor should state his opinion to the questioner, but he should also indicate the other opinions, if there are any. However, here it appears from Rabbi Melamed’s summary that there is no one who permits it (I did not examine the opinions myself).
I think it would be worthwhile to speak with the Efrat organization, headed by Rabbi Dr. Schussheim. I think they have all the relevant information (about adoption, etc.), and also persuasive methods backed by extensive experience with mothers in various situations.