I was a Freshman last year (in a somewhat similar situation to OP's girl - I graduated early), and most of my friends are over the age of 22. Most people are surprised when they learn my age and I rarely feel less mature than my friends. Most Freshman girls are not mature (I sometimes wanted to shoot my old room mate and her friends), but there are exceptions to the rule.
Then again, I could just be immaturely proud of my older friends....
OP: There is one important thing you've failed to mention; does this girl like you?