I honestly think it depends on your parents. I'm a really responsible kid so my parents trust me with a variety things, including being able to take care of myself in certain situations. I don't think it's too young, and I'm 15 myself. I know that there will be creeps at conventions, but I'm always with 5+ friends when I go to them, and we NEVER go anywhere without a buddy. I'm planning on cosplaying a Magi character who's djinn equip is like a bikini with no jacket or anything and I know I will have to protect myself when I go. This means I will switch costumes in the middle of the day so I won't be half-naked and walking around at night. I'm also going to be wearing an extra layer under the top just in case something happens.
Also, it's sometimes the person who wears the costume that makes it super inappropriate. Don't go around making sexy poses in the costume and don't agree to anyone who asks you for a photo that you deem inappropriate. If you feel uncomfortable around someone, just leave. You're the one who's wearing the costume, so you're the one who decides what you're going to do.