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.
Just enjoy the ride, no need for labels.
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