Interviewers often ask what kind of pets a veterinarian candidate has. This is not a prerequisite for the job but does show that the roots of your interest in caring for animals run deep. This is an opportunity for the interviewer to find out what interests you.
"I think a better question would be 'what animals do I not have?' I have two cats, three dogs, horses, and my husband raises cattle. My family jokes and says I have to take care of other people's pets to be able to afford my own."
"I have two boxer dogs. They are my babies! I have considered adding another puppy to the family, but haven't made that commitment yet."