Brian -
Technically, it's your parent's business. You may be doing all the work, both at a show and behind the scenes, but, legally, it's their's.
For the record, if your parents are OK with the legal situation, as well as allowing you to do this, then I don't see a problem.
My only word of advice / caution is this: When talking with a client, should your age come up, say something like this: "I'm under 18, so you'd actually be booking my parent's entertainment company. But I'm the only DJ on staff. So, I'll be the DJ at the event." etc.