Don't forget, though, that 'zoo permits' only apply to native wildlife. If you want to have a zoo that only features exotics, you don't need any permits, but watch out for the local by-laws.
Are you 100% sure about this? I ask because I looked into this in detail and the answers I got were quite different. I live in Quebec though, that may be where the difference is.
From what I gathered, to get a zoo permit you have to send in with your application: the species of animals you plan to have in your zoo and very detailed plans of the whole zoo's installation. Reptiles and inverts don't require a vet on staff but apparently, other types of wild (non-native and native) animals do.
If they approve your plan and your zoo facilities, you get your permit.