I don't know exactly how your fair works, but at mine there is a junior fair (4H, FFA, etc.) doe and litter project. How it works is the youth must be taking a "breed rabbit" which is the single entry purebred rabbit that is entered in the junior fair rabbit show. Once they have taken the "breed rabbit" project for a year, they can take a doe and litter project in which the youth breeds their doe during a certain set of dates so that the kits are between 6 and 8 weeks old for fair. The entire litter and the doe is brought to the fair and is judged based on how many kits the doe raised, how well both the doe and litter conform to the breed standard with the kits ideally being of better quality than the doe (showing that you are working towards bettering the breed) and as many of the kits being showable as possible. They are also judged on both the doe and kits' flesh condition, which tells how well she produced milk to feed the kits and how well the doe handled nursing the the kits, as well as how clean and well cared for both doe and kits are.
This is my first year out of 4H and I always showed rabbits at our county fair through it, as well as showing at ARBA shows. Now that I am out, I won't be showing in the open category, as at our county's fair, most breeders don't enter rabbits because they want them to be judged, but because they want to sell them. So almost all of the rabbits in our open rabbit barn are culls (I'm using cull as in a rabbit that the breeder wants to get rid of). I don't even like to go in there for risk of picking up a disease. Our county fair open rabbit show isn't ARBA affiliated in the least and the rabbits aren't even removed from the cage for the judging. They just walk around and put stickers on the cage cards to note placing. Maybe that's how all open county fairs are?