well you can shoot for a degree in something that will help you work at a zoo or an aquarium. But warning it doesn't pay well at first.
I use to volunteer at the Wildlife World Zoo in Phx, I worked as an asst. keeper in the small mammal exhibit. LOVED IT!! Was actually offered a job as the reptile keeper. But at the time the thought of taking care of snakes freaked me out! (crazy huh...lol) Plus I think it paid about 22K a year. That was about 10years ago. It was a very fufilling job...and I had fun every single day I was there. Would love to do it again but my family restraints probably would not allow for it now. So...I will just build my own zoo here...lol
I do have a friend out here in Tucson that works for a wildlife rescue. She started only volunteering and then was offered a full time job. So ya never know... Do what you love!!
Oh yea I forgot to say...I had no formal training with animals...just have this natural thing with them...always have since I was a little kid. My mom has some great stories of me with wild animals....once playing with a skunk (apparently I thought it was a black and white kitty)...going up to really agressive animals...never been bit. She said that she was always scared because I would just take off before they could stop me.