Match your current skillset against the typical requirements. There's a heck of a difference between a receptionist and a nurse, for a kick-off. Which are you after?
I applied for a job as a receptionist after passing my animal care college course with distinction and have office experience (although no reception experience) but unfortunately didnt have what they were after :-(
I woundnt say you need to, but I would think qualifications and knowledge of animals, plus previous reception work may be a good place to start.
PS: Here's a hint -
If you get as far as an interview, don't simply say that you love animals. (All the other applicants will say that). Stress that you enjoy working with people, that you understand that many of the people bringing their pets to the surgery will be extremely distressed (especially if their pet has to be put down) and that you believe that you'll you'll be able to help them cope with the stress of their visit.