Nobody should ever just get thrown away. It's one of the hardest things to grow up even CLOSE to that, can't imagine how much worse it must be when people think there's a "reason" they can treat you badly over something they think's "wrong" that you didn't have anything to do with other than being born.
You finding her, and caring enough not to leave her is already improving what happened to her, and that is pretty fantastic stuff. If you have what you'll need for her, then I would say it was a good idea.