At my facility, there is a 2 year period that must pass before an outside relationship is considered legally okay. However, even then, HR has made it VERY clear that no matter the time-frame, dating a former patient would be HIGHLY frowned upon by the facility. You need to check with your own company policies.
That being said, I think this is a bad idea. Unethical, for starters. And as others have said, this girl clearly has other, more important issues to deal with. If you actually care for her, you'll do what's in her best interest.