Moving is a normal part of life, and it's quite common for families to live in a few different houses as their children grow up. However, what is usually a fairly uncomplicated event when married can turn into a full-blown custody battle after a divorce. In most cases, the problems occur when it's a custodial parent who is relocating and the new house is a good distance away from the previous location.
While the courts cannot stop a parent from moving, they can prohibit the child from being moved away from another parent. In general, the courts do not get involved unless the proposed move would move the child more than 50 miles away from the previous residence. In cases where the two parents already live far apart and the move puts the child closer to the noncustodial parent, the distance may not be an issue at all.
However, when the move will take the child farther away from the other parent, there is the understanding that this may also impact the ability for the other parent to have their parenting time. One of the best courses of action in these cases is to attempt to discuss the situation with your ex and explain the logical reasons why the move is needed — moving to get a new start or because you don't want to deal with your ex are not usually legally acceptable reasons.
If your ex agrees to the move, you just need to notify the courts of intent to relocate the child and the agreement of both parents. A new visitation schedule may also be needed. However, if the move is contested, you will likely need to talk to a Florida family law attorney about what to expect from the family courts.