Here is a list of acceptable IDs:
http://www.tsa.gov/traveler-information/acceptable-ids
Note that it says "18 and older" giving you some wiggle room. Althought I expect that's because they anticipate an adult will accompany. It also says that if you don't have ID you can still travel but (expect to be hassled, effectively).
Interesting that a weapons permit is not considered "acceptable ID" to get on a plane.