I was under the impression that you must be registered with AKC in order to compete in their venues...
But there are other organizations that may allow unregistered dogs to compete. I'm new at this so I don't know much about the different ones. I do know that recently AKC has initiated a program where mixed breeds can register and compete. I've been getting their e-mails about it. I think it's called Canine Partners. If they have that there has to be a way to register your Purebred dog too.
Edited to add... just looked on AKC's web site... this may help answer your question.
Purebred Alternative Listing/Indefinite Listing Privilegehttp://www.akc.org/reg/ilpex.cfm