I would say no - It's not worth it. The only reason I say this is because you are in a similar situation that my nephew was in.
He started dating a girl that was 15 (freshman in high school) and he was 17 - almost 18 (Senior in high school) They dated for 2 1/2 almost 3 yrs (she is now 17 and my nephew is 20 - she is senior) After my nephew graduated from high school he started working and going to college. He still lived in the same town (he didn't go away to school) so he still saw her almost every day. After awhile, he matured to the point that he didn't like doing the same things she liked to do. She wanted to go to the football games and all the high school dances (Homecoming, Prom etc,,,) and my nephew just isn't in to that kind of stuff anymore. He knew it wasn't fair to either of them if he stayed in the relationship because she needed to experience all those high school things and he had already "been there, done that". It was hard for my nephew because he is a very soft-hearted caring person, but he broke up with her.
He is now living on his own and started dating a girl his age. He is much happier and knows in the long run it was the right thing to do.
In a few years from now your age difference won't be a big deal, but I think right now it is. You are old enough to go to a bar and she's far from it. Besides, if I were her mother, I would have a heart attack.
I think you should try and find someone closer to your own age.