Legal Question in Family Law in Florida

Not legally, without court permission to relocate.

Fine, thank you. You really haven't given much information about your situation, not even whether you're married to the father, so I'll assume you aren't. If you move out, the father may file for paternity and (what used to be called) custody. Of course, child support and visitation will be established based on who gets custody. Florida law doesn't permit you to move your child more than 50 miles without permission of the father or a judge. There is a certain procedure, and possibly a lawsuit, that must be filed to get permission to move more than 50 miles, and you should know that judges are extremely reluctant to grant permission to move.

No. You need court approval to remove the child from the state and thereby frustrate the father's visitation and custodial rights. Judges do not lightly let you take the child away from the father.