Their are 2 kinds of chihuahuas, appleheads and deerheads (reindeer? ). Both forms are within Akc standard. They are worth breeding if you like them. However Appleheads are more popular.
Breeding should only be done by reputable breeders who show their dogs and breed to improve the genetic stock. I've never heard of a reindeer chihuahua, so I doubt they're AKC.