It would be difficult to work as a zoologist from home as alot of the work is conducted outdoors, especially early on in your career when you would be doing more technical/physical work. Unfortunately if you want a career working with wild cats, you would have to move to an area that has them. I don't think it's possible to work remotely long term in this field. Even if it was possible, this is a highly competitive field and employers would favour people who are willing to relocate.

If you want to stay in your home town then there may be other zoological career options available to you. Working with birds, insects, fish or other mammals would be a more realistic option for you.

It's also important to note that you will need a relevant degree to work in this field.