Most Helpful Guy
It's too soon. I know your gut might say that things would work out, but you have a very very low chance of that happening. You can try to make her your girlfriend when she gets over the guy, but not now. She maybe attracted to you, but she's still in love with her ex. I'm telling you this based on experience, don't jump the gun. You'll just land yourself in a world of hurt if you fall for her.
If you still want to go ahead, at least take things slow. She will try and replace him with you and she'll try to fill that void as fast as possible. Don't fall for it. Take it nice and easy.
It's understandable up to an extent to be friends with your ex. If the worrying becomes too much on her part, or she talks about the guy too much, take a break from the relationship.
No one deserves to be fed someone else's crap.