Just a quick thought. The OP can register them with the "joke" organizations, mainly Continental Kennel club. Most pet stores are now buying puppies with Continental Kennel Club papers because they have no restrictions and any back yard breeder can get them on their dogs. So, she can breed her wonderful dogs, register them Continental Kennel Club and sell a bunch of back yard bred puppies. Yea, great.
. Your rabbits and such win shows, would that be 4-H shows or county fairs?
You won't be showing or competing at AKC shows with your dogs. You can't just "talk to someone about registering them" with AKC, the sire/dam had to be fully registered before breeding, then the litter registered. But, as I stated above, there are many many "joke" registries made just for "breeders" like you who want to register the dogs before breeding so they can make more money on selling the puppies.
Also, your girls are LITTERMATES, not TWINS................ At least get that much correct when becoming a breeder of dogs.