Be brave, Kay! If you've already been thinking about a change, this sounds like a perfect opportunity! If he's alrady interested, I say Go for it! It is working with animals, and that's something you know you enjoy.

The job you're working at now is a fine "first job," but they really don't expect someone your age to stay long-term, despite what your boss said to you. Do plan to give two weeks notice, to be polite, and I bet if you do get the vet office job, everyone will wish you well.