Sounds like she already is. I'd stay the course and not specifically ask for a "girlfriend" commitment.
That's great and I think she would love to hear that,some girls can't wait to hear thoes words,there is something that makes a girl feel she belongs with you.
I like what vintagefit1987 said, just let her know you ant to be exclusive. That leaves the label off but lets her know you don't want to date others
ask her tomorrow