I would be very, very, very careful about approaching a relationship so soon after a breakup. There is that whole "rebound" period where people will grasp on to anyone who seems caring or better than the last guy and do you really want her decision to be with you to be based on those emotions?
Offer her a place to live, let her get her life straightened out, THEN approach a romantic relationship.
That's what I recommend anyway. I feel like trying to get someone in a new relationship while she's still trying to end one is a recipe for drama.