It's only a problem if you make it into one.
I'm currently seventeen, turning eighteen in March. My ex is fourteen, turning fifteen in February. I was in the same boat as you.
My friends didn't like it at first, but they grew to accept it because well, they were true friends. Age isn't really a problem to my family, as long as we follow the 'rules.' I dated her because I had genuine feelings towards her as we attended the same church and saw each other for the good part of the week, as our youth group always attended special events and visitations. I'll probably get flamed for posting this, just as you somewhat were. However, I could care less what anyone on this site thinks of me.
As for personal advice; love doesn't pertain to any ages. Ask around in your family. I guarantee there are some people whom's spouses have a greater age difference than you and that girl.
Take the risk, enjoy your life. You don't know what you could be missing out on if you turn her down. If your 'friends' don't accept you, they aren't friends.
Everyone deserves to be happy, no matter their age, gender, race, sexuality, etc. So go for it, young padawan.
Just don't fuck her.