It's a generous impulse, but I think you need to think it over more.
It sounds like you'd be basically offering the girl the same thing her parents are, but in a different location - free room and board, and some babysitting. So aside from a better choice of schools, there would be no big difference in her ability to attend a trade school compared with where she is now. She'd still have the problem of going to trade school while working part time at multiple jobs, and paying for full time daycare (I'm assuming you're not offering to babysit 10 or more hours a day, which is what she'll need with job and school). Plus, she'd be living away from her family and existing support structure.
She might be a good kid who made a bad decision, and will work really hard given an opportunity. Or, she might take advantage and go out partying all night while failing her classes and leaving you with the kid. The problem is you don't know, because the only thing you know about her is her Facebook page.
I'd suggest contacting her on Facebook to offer *moral* support at first. Chat with her, get to know her, hear more about what her life is like. Then you can meet her in person, and see the reality of her life - is she hard working, or just hard complaining? Does she give up easily? Does she have a realistic view of just how much work going to school, working, and looking after a baby really is. How much are her parents actually doing to help - it may be more than you realize.
Once you get to know her, and her situation, in reality rather than just Facebook, you'll have a much better idea of the kind of help she really needs, and how it fits into her life.