The main purpose of the American Kennel Club is to maintain a pedigree registry of purebred dogs, which aids the AKC's mission to promote and improve the world of purebred dogs for companionship and sporting competitions.
If a dog obviously looks purebred but is uneligible for American Kennel Club registration because its parents are either unknown or unregistered, the owner may apply for an Indefinite Listing Privilege (ILP).
Ideally, the best dogs win, and the lesser dogs are weeded out of future breeding programs.An AKC dog show is sanctioned by the American Kennel Club, the largest single registry for purebred dogs in the USA.
I have always recommended that all of my friends and my readers here at LTK visit the American Kennel Club website if they are thinking about adopting a dog, especially if they are looking for a purebred.
The breeding plan you're currently considering will not produce purebred cats, and your kittens will likely be less desirable to the buying public than a purebred kitten of either breed.