Florida follows the Uniform Interstate Family Support Act (UIFSA). Many people are confused by the requirements of UIFSA. The basic rule of UIFSA is that the state which originally issues a child support order has continuing exclusive jurisdiction over the case. That means that no other state is allowed to change the original order - any change has be done in the original court.
Only if neither of the parties lives in the original state any longer, is it possible to modify child support in another state. The Fifth District explained the procedure recently in this case. Chapter 88 of the Florida Statutes is where you find the law on UIFSA in Florida.