It took me a few days, but I have your answer. I finally called the Cape Hatteras National Park Service (252-473-2111)to get the straight answer. The nice lady who answered the phone was also stumped. She had never been asked that.
She decided to call John Denson who told her there was no age policy. So, as long as you can pay the fee, you can camp. Have fun and bring your bug spray!