Is it a state law in Florida that your insurance company must provide a rental car after an accidentif you have full coverage insurance and hit a deer?

No. By "full coverage," I assume you mean you have comprehensive and collision coverage. This does not include rental. You have to buy a special endorsement on your policy to get rental. Hitting a deer is a comprehensive claim and if you have rental, you will get a rental if the car is non-drivable or when it is in the shops for the repairs. If you did not buy rental, the insurance company does not have to pay. Check your coverages.