Make sure she knows your expectations and you know hers right from the start. Put them in writing if you have to.
If you choose to make this decision, definitely put it in writing.
I'd also have a talk with her parents first and let them know what assistance, specifically, you will be providing. And as others have suggested, get to know her much better, in person, before taking the final step.
You could also ask them now, what help if any you could provide.
If you are in a position financially to help her out with necessities such as diapers, etc., that would probably be a big start and might free up some of her cash to help her improve her living situation somewhat. If this help is gratefully received (and responsibly used) then if you are in a position to finance other things so that she could at least give up one of the crappy jobs, gain some skills, and perhaps attain a much better, higher paying position, that would be good too.
Also, just encouraging her to check out schools (especially those offering distance education and online options) would be a good thing too.
While I agree that she has parents who are helping her, I do not agree with the "you made your bed, now lie in it" when children are involved. Tell the parents you'd like to help and ask for suggestions.
I do not think it is a creepy/weird idea at all. My SIL got pregnant, quite unexpectedly, in her early 30's and the father (her boyfriend) abandoned her and the baby. (She is now happily married with more children.) She has mentioned a number of times that she was exceedingly grateful for the help she received from family, friends, and a local crisis pregnancy center. She has also said how she didn't see how she would have gotten through it if she had been in her teens, with few, if any, job skills. I see absolutely nothing wrong with helping. I fail to see the nobility in suffering, struggling to make one's way, etc--unless the help offered is taken advantage of in an inappropriate way or someone feels entitled to it.