I'd think that either Zoology or Biology as a major and business as a minor would be an excellent combination. As Robert says, experience (and learning from it ) is going to have a lot to do with success, but being able to manage a business budget, handle taxes and paperwork, calculate the value of investments (both fiscal and physical), organize all your valuable information, provide the needed husbandry in a cost-effective manner, etc., all these things need to be balanced in order to be a successful breeder, and your performance at any one of them can significantly impact your business' success, so even if you don't get a degree, some classes or an internship period would probably be highly beneficial.