I personally don't think you're too young. As long as you have a good reason for wearing the costume other than it being skimpy.
I was 15/16 when I wore Yoko Littner. Yes it was super skimpy. But Yoko was a character who I passionate about because of her attitude. Today I still think she is one of the strongest fictional female characters ever.
But of course if you're parents don't like it don't go against them, you can try to convince them, but don't go behind there back.
Other than that I think everyone's suggestions have been great! Good luck!!