If the father will not consent, you will need the court's permission before taking the child out of the state.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.
I do not practice in FL, but I may offer some general advice. I agree with the first answer, as long as the father has been adjudicated (legally determined to be the father). If the father has not been adjudicated, then you likely do not need the court's permission and may just move. The father has likely been adjudicated if he pays child support. If you receive financial aid from the state not paid by the father, then he likely has not been adjudicated.
If you do need the court's permission, you will have to give notice to the father, and the father will have an opportunity to object. If the father objects, you will then have to convince the court that moving is in your child's best interest.
Consult directly with a local, experienced family law attorney for more specific advice. And before taking any action, you should confirm this advice with a local, experienced family law attorney.
Good luck to you and your family!