I was pretty sure you were that kind of person (over thinking and analysing... same here!!).

Well, I think that depends on her capacity to be involve in an intimate relationship because your willing to be with her is really there. It's important to have a proximity. You want to grow with her, to build something. It's at your best advantage.
I think the worst thing you could do is to be invasive because you'll her push away. Some people don't have the same needs.