I live in a high incidence area for Leptospirosis in Illinois, so we get the vaccination for Bella. She hasn't had any problems with the vaccine at all. It looks like Florida may also be a high incidence area. I would go with your vet's recommendation. Here's an article on Leptospirosis in Florida:
http://miami.cbslocal.com/2017/03/01...em-in-florida/