I think it's a wonderful idea and not rude or creepy at all.
That said, you're looking at making a potentially huge investment on your time and resources. I would advise going slow, and take the time to get to know this young woman and how she manages her life and cares for her child. Is she serious about going back to school? Has she researched her options or is she looking to sign up at the first for-profit "university" that advertises on TV?
Maybe start with something less taxing on yourself, like offering to review a resume or help her with getting a single full-time job that might pay a little bit better than she gets now.