Based on what information? At best they have it as a CAT 3 hitting FL right now, if it hits. We're 5 days out and most of the new models have it going east of the state. The track has shifted quite a bit because they take the middle of the trends.
Hitting CAT 4 out in the Atlantic means almost nothing. A hurricane has to go through a lot of islands and gets broken up by Puerto Rico mountains before it gets here. It's going to be a lot of rain and wind, NBD.
IMO it's far more disruptive and annoying to drag your family 1000 miles away for a day of rain and wind then it would be to just stay where you are and deal with it. If this was a CAT 5 in the Gulf heading east, it'd be a different story. Atlantic hurricanes are a major pain to the island nations, but there's a LOT for them to go through before they get to FL.
@JOhnH you have to do what is right for your family, of course.