Good for you, I mean it.
Never forget the premises though. Being self harming and suicidal is not something you can suddenly flip a switch on. Chances are she's not healed completely, if at all... and you're going to have to be the person to deal with these things if you enter a relationship with her.
So yeah.. be a little wary. I don't know what year you're in but she's been with this guy for some time and had several other boyfriends... what gives? do these "relationships" all last a couple of weeks?
Starting early is all fine and dandy, but being unable to say no to anyone who looks your way (that's the impression of her you've conveyed) and being needy/thankful for it, are not trademarks of a good relationship or healthy perspective on relationships.
It is a bit perplexing that she seems unable to be by herself. Probably a sign of very very low self esteem and insecurity.
In other words, you might just be biting off more than you can chew.