Good Morning Rachel
As of right now, and for the foreseable future, the Biewer is not accepted in the AKC and so can not show with the AKC. Presently,the venues available for them to show are the NAKC, the IABCA and ARBA.. there maybe others, I believe there is something in Canada, our Canadian friends maybe able to help us there..
I have shown NAKC and IABCA, they are both very different from each other and different then AKC. ARBA is now another venue available and I'm sorry I don't know as much about that but I'm sure they also have good information available on their website.
Each of these organizations have different names for their titles and different qualifications for earning them and many diffrent venues where their shows are held. My experience is that the shows are alot less "formal" then AKC shows, the judges give you and your dogs critiques and will give suggestions if asked. It's been very exciting and a great place to start learning how to show a dog without the "fear" of doing it wrong, as the judges are there to help you if you ask.
Here are the links for you to follow, this should get you started...
http://www.iabca.com/ http://www.arba.org/ http://www.raritiesinc.ca/
-Diana