Congratulations on moving! Enjoy soaking up the sun’s rays to your heart’s content. To answer your question, you don’t need renters insurance in Florida, legally speaking, unless your landlord requires it.
For the cost of one coffee a week, you’ll get hundreds of thousands of dollars of protection for your personal property, covered living expenses if your apartment becomes uninhabitable, and assistance with legal fees if someone gets injured in your apartment or due to your pet.