I'm excited that you want to work with exotic animals. I'm the head zookeeper at a private exotic zoo in the Houston area and I love working with exotics. The thing about being a zookeeper is that in big zoos, you typically specialize in only one species. For example, you'll be the keeper for just the giraffes or just the elephants. The zoo I'm at is smaller so I have the opportunity to work with all the animals (bears, wolves, hyenas, primates, reptiles, bearcats, large cats, birds of prey, otters, tropical birds, hoofstock, etc). Being one of the head zookeepers, it's necessary for me to be trained on all the animals so that I can step in and take care of them when their normal keeper is on vacation or out sick.
When I was in high school I did an internship at both a vet clinic and the zoo I now work at. I found the vet clinic internship to be boring as we mostly just saw cats and dogs all day long and I found it depressing to sit with pet owners while their pet was being euthanized. Being a zookeeper is hard work but find it very rewarding to be cleaning out a primates enclosure while they're hanging on my shoulder grooming my hair. Zookeeping is not all fun and games though...in addition to building enclosures, creating enrichment games, cutting diets, administering medications, hand raising animals, etc. we're also responsible for cleaning and repairing the enclosures and we work in 100+ degree weather, rain, etc. I still prefer it over working with domestic animals.
Here's a website that has suggestions of jobs that involve working with exotic animals. https://study.com/articles/Careers_Working_with_Exotic_Animals_Job_Options_and_Requirements.html