Yes, you can show your dog in AKC agility with a limited registration, as long as the dog is registered with AKC. There are other agility venues that you can also compete in: Canine Performance Evenets (CPE), US Dog Agility Association (USDAA), Teacup Dogs Agility Association (TDAA), and others like NADAC, etc. They all have websites. There is an excellent agility magazine you can subscribe to called Clean Run.
My male cavalier, Geordie, is registered with the first 4 venues I listed above. He is 13 inches at the withers, so he is in the 12 inch class. In USDAA, he would have to jump 16 inches in their championship class, but I will only show in in the performance class at 12 inch jumps.
One thing you should know - AKC allows dogs to begin to compete at 1 year of age, but I would wait until the dog is 18 months old to jump at full height!!! You want your pup to be fully mature before competing, or you could damage his hips!!
In fact, when Geordie was one year old and we started beginners agility classes, I made sure the jumps were set at 6 inches to avoid stressing his joints.
Right now your puppy is too young to go for long walks or to be doing any jumping or much running. His little joints are growing, and too much exercise can cause hip dysplasia. But you can reward (click and treat)him for approaching, sniffing, and pawing agility equipment, which will make it easier for future agility training! My pups took a puppy class called L'il Sports, which introduced a teensy bit of agility, flyball, and rally-o.
