Dude, just go day by day and don't worry about it. I had plenty of relationships...and all the ones that started like: "Will you go out with me", or "Will you be my girlfriend"....all that corny BS.....ended soon after and it was just too much too soon.
Just take it day by day, spend your time with her, but not too much time, give space, give yourself space and just feel it out man! That is what I did with my current...and hopefully permanent girlfriend. I met her when I was 21, she was 19. It was on for 4 months with no "title"...then off for 2 years+....but we still talked as friends.....and now I am 25 and she is 22...and things couldn't be better. We have been strong for one year. One year doesn't seem like much, but see we have 2-1/2 years under out belt as friends or friends that date....etc. We know everything about each other. We know what he want, what he had, and what we don't want. We never put a title on it, but one day, we both just realized it is for real now...and it better be with all of the things that we do together! hehe When her family is sending you B-day cards and holiday cards and you are going to family functions every week...IT IS REAL!!!