Whether or not Peter Pan was Jewish, it seems he could never become Chayiv to perform Mitzvahs. Being that a person requires Da'as to convert, could Peter Pan ever convert to Judaism if he never grows past 12 years of age? Or is Peter Pan forever stuck being Patur from Mitzvahs?
I'm afraid Peter Pan is still חייב in מצות. The law that a קטן is פטור from מצות is based only on age, regardless of actual physical maturity. An איילנות - a girl who never reaches physical maturity, still will become a גדולה eventually.1 Therefore, while Peter Pan never physically grows past 12, he will still be חייב in מצות after his בר מצוה.
And if you'll say that his name is פטור, so he must be פטור in מצות, well that may be true, but we apply the principle found in ש"ס of פטור אבל אסור; meaning that he is only פטור from punishment if he fails to do the מצות, but it is still אסור for him to do so.