I would love to go to school to become a veterinarian.
A vet is a wonderful job. It's actually veterinary physician, shortened to veterinarian or veterinary surgeon which not many people know!
How long do they have to go to school for?
Most likely a couple of years. It's the branch of medicine so probably as long as regular general medicine. The difference is it deals with animals not humans.
I love animals and caring for them.  I would mostly like to work with dogs.
There is many branches within veterniary medicine itself. Some are general practice and some may be specialized like livestock, zoo animals or equines. I'm sure you'll find something for yourself.