As everyone else said, there's no lower limit on the age at which someone can cosplay.
At your age, your parents won't be too keen on you running about in a crazy costume among a bunch of older teens and adults. If your parents see you as responsible, they'll probably be more trusting of you to make good decisions, but if you're irresponsible like I was at your age, your parents will likely throw a wet blanket on the idea before you can even get started.
So if they say no, don't whine, don't fight, don't act like a little kid about it. Be mature. Don't just be mature for a day, you have to commit. If you want to convince your parents that you're capable of making good decisions, you have to go all the way. Don't nag at them if they reject at first, just keep at it. If after a month or so you think you've done a good job at being responsible, ask them again in a very diplomatic manner. They should be more receptive to the idea if they think you can handle yourself.
Then once you get there you can spaz out and be a crazy geeknerd. :D
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Want to help create a US anime convention map?
COSPLAYS IN PROGRESS
Canterbury (Kuroshitsuji) - 30% - Kuro Gathering
Utatane Piko - default (Vocaloid) - 15% - Ohayocon
Boris (Alice in the Country of Hearts) - 3%
Jean (Shingeki no Kyojin) - 0%