Yes, if you have a valid injunction for protection against domestic violence in Florida that meets federal standards you can get it enforced in another state. Under the Violence Against Women Act, all valid protection orders in the U.S. get recognition in all state courts within the U.S.
In order for your injunction to be good anywhere in the U.S., it must meet a few requirements.
First, it must have been issued to prevent violent or threatening acts, harassing behavior, sexual violence, or to prevent another person from contacting you or coming near you. The court that issued the order must have had the proper jurisdiction over the people and the case.
Finally, the domestic abuser must have gotten the proper notice of the order, and been given an opportunity to go to court, even if he or she chose not to appear.
If the protective order meets those requirements, it is valid in other states and must be enforced the same way that state enforces its own orders. If the abuser chooses to violate the out-of-state injunction, he or she will be punished according to the laws of whichever state you are in.