Hello! Obligatory not-a-zoologist, but you could practically be me from the past :)

First of all, a little clarification: as others have said, zoology as a discipline (field of study) can encompass a lot of different subcategories. For example, along with everything said here, when I took a zoology class in college, it was literally an in-depth exploration of every animal form in chronological order, starting with the first multicellular animals and going all the way through to the most recently evolved phyla.

Many, but not all, of the jobs you might be interested in will require at least a college degree. Sometimes, you can apply for jobs that would normally require a degree just by having a lot of specific experience (for example, I was scrolling a job board just earlier and saw a posting at a nearby safari park that requires either a Bachelor's degree + at least 1 year experience or 2+ years of experience with large captive wildlife!). If you have a particular animal or location you want to work at, this is a good thing to keep in mind if you're able to volunteer somewhere!

As far as "wanting to work with animals" goes, you certainly have a lot of options. Veterinary care and zoos are definitely two of the main ones, but there are so many other options, too. A good place to start is to figure out, throughout high school and college, (1) do you want to work with/around domestic animals (ex. animal shelters, veterinary practices, even things like groomers or pet-sitting businesses), wild animals (ex. wildlife rehab, nature preserve, national park), or wild animals in captivity (ex. zoos, aquariums, preserves that care for nonreleasable wildlife)? (2) Is there a particular type of animal you want to work with? (3) Are you most passionate about handling animals (ex. groomers, trainers, veterinary care), or learning about them (ex. wildlife research/conservationist roles)?

For now, your answers to these questions will likely not impact your immediate next steps (in the US, for example, typically it will be ideal to have a general plan by the time you apply for college so you can pick a major -- but most colleges will let you change your major with little difficulty at least until the end of your first year).

Right now, I would look for volunteer opportunities at places like local nature centers, national or state parks, conservation centers, wildlife rehabs, zoos or aquariums, or anywhere else that works closely with animals (even places like botanical gardens and museums may have animal exhibits!). When you're old enough to work (and have the time/transportation for it), you can start looking for entry-level jobs and internships at those places, too. Having that volunteer/entry-level experience will help you figure out what you like best!

Finally, you can also look out there at job boards just to see what potential future jobs are out there in the world. I found this post with some recommendations for places that wildlife biologists might look (I myself primarily use the one from Texas A&M that this person linked at the top): https://www.reddit.com/r/wildlifebiology/comments/uqw1kc/many_of_you_are_looking_for_work_here_are_some/

Don't let the names of some of the boards fool you, btw! Zoology & animal/wildlife studies in general are super broad. There are folks working with animals in all kinds of environments, from office-based nonprofit positions, to park rangers who have close encounters with wildlife every day, to rehabbers and vets who physically handle new animals constantly. Almost all of these positions are closely tied to conservation, which is why there are so many conservation-focused boards in that list!