Does a dog have to be pedigree to partake in a dog show?

For conformation, which is what I'm guessing you are talking about requires that the dog be registered. In most countries and registries that also have to be intact. In order to win, it helps that your dog be an excellent representative of its breed, well trained for the ring and well groomed. It also helps that the handler knows how to handle the dog in the ring. Now this is for the US. Australia might do things differently. You might have to talk to someone in your local kennel club. Google will help you here.