I understand your concern for the safety of you and your daughter.
Based on the information you have provided you should be able to leave the state without seeking the permission of your daughter's father. However, you should still consult with an attorney privately for a full analysis.
Below is the link for the Florida Statute you might want to review:
744.301 Natural guardians.—
The mother of a child born out of wedlock is the natural guardian of the child and is entitled to primary residential care and custody of the child unless the court enters an order stating otherwise.
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If you were never married to the father and no paternity action has been commenced by either of you (and based on your post it does not appear that such action was filed), then you have all the decision-making authority over your child and all the time-sharing. As such, you may move without permission from or notice to the father. However, the father still has the legal obligation to financially support the child. Good luck!
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I agree with Attorney Tomshinsky, if there is no paternity established in a family law court, then you have all the rights regarding the child according to Florida law. Consequently, you can leave and go wherever you want. However,the boyfriend can file for paternity and request that you return the child to the jurisdiction so you need to establish residency wherever you intend to move. Preferably to a state with a minimal residency requirement like 6 months. Good luck.
B. Elaine Jones, Esq.