After your last thread about hookah girl, I was wary about opening this one :)
Others have given you great advice. Don't invite her to your home. As a woman, I would never trust someone who moved that fast with me. I certainly would not go. (Well, maybe as a dumb, naive girl). Plus, for your own safety, get to know someone at least a little bit first.
I like the idea of calling her and asking her out for coffee or a drink, or lunch. Lunch is more casual than dinner and not pushing it too fast.
So I guess slow and easy is my advice.
I like this thread much better than hookah girl, btw :)