The job you are describing--taking care of animals in a zoo--is a zookeeper job, not a zoologist. A zoologist is basically a biologist who specializes in animals, not plants. So a zoologist could study ground squirrel genetics, or how stress affects relationships among baboons. Zoologists are usually researchers. Some larger zoos employ researchers, so you could major in zoology. But that will not train you to work in a zoo.
Zoologist Job Description, Career as a Zoologist, Salary, Employment - Definition and Nature of the Work, Education and Training Requirements, Getting the Job
If you want to be a zookeeper, you need to know some biology, but also some basic veterinary medicine and, depending, on whether you want to work directly with the animals or run the zoo, some business management skills. Many zoos have to work very hard to bring in donations and other funding, so some knowledge of "development," getting people to give you money, would also be useful. If you want to focus just on the animals, I would recommend learning as much as you can about comparative animal physiology and animal behavior, diseases of wild animals and diseases and conditions of captive animals
I would recommend that you pursue all of these aspects over time to make yourself as valuable as possible. But start with the parts that are most interesting to you, to keep your enthusiasm up.
According to this website, low level zookeepers don't make much money.
Zookeeper
Also check out the links at the bottom of this page--to zoos, etc.
Zookeeper - Wikipedia, the free encyclopedia
Good luck!
PS. Don't forget to learn something about plants as you go, because a lot of animals eat plants and you can understand how animals and plants interact better if you understand where plants are coming from.
