If you are not married to the father, and he has not taken you to court to establish a time-sharing then you may move. However, he can stop you from moving, and force you to comply with Fla. Stat. 61.13001, by simply filing a petition to establish paternity and asking the court to establish time sharing. I've attached a link to the statute, take a look at paragraph 1(e).
Sign up to receive a 3-part series of useful information and advice about child custody law.