To briefly answer this question, a parent who has majority timesharing with their child(ren) may move out of state. However, there are a few hoops that need to be jumped first.
Specifically, Florida law requires parents who want to relocate with their children, thus moving more than fifty (50) miles away from the minority timesharing parent, to file with the court a Motion to Relocate. This Motion must be heard and granted by the Court prior to relocating.
Thus, if you are considering relocating with your child(ren) you should consider contacting a Jacksonville Family Law Attorney for assistance in the required court process.