This is going to get loads of dislikes but thinking back to when I was 15, I think I was pretty mature and dated a couple of lads who were 19 - 21 and got on much better with them than I would have done with anyone my age. I wasn't in school though and I was going out to bars and looked about 19 aswell though so that probably had something to do with it. I didn't see a problem with it at all then, niether did any of them or their friends, it wasn't really an issue.
I'm 20 now and thinking about it, it does sound wierd and the immediate response in my mind is "that's wrong". I suppose it's whether or not you like her enough to break the law.
Also you've got to think about whether she really likes you too or whether it's the fact of dating an older guy, admitedly it was probably partially that for me at that age.