You don't have to "send him" to a trainer but you can, and should, enroll in a training class with your pup. Agility is more than just having your dog do the obstacles--that's the easy part.
AKC started allowing "all american" (mutts) to compete but they do have to be registered and not all competitions are required to allow them so check before hand. There are also quite a few other agility organizations--CPE, USDAA that always allow any breed/mix.
Just reiterating what Shane said - getting your dog to go over/through obstacles is the easy part. It's the attention, self control and handling that makes the sport as special as it is. If you ever want to take it seriously, I would highly recommend you attend a class or two with your dog designed for beginners.