Picture this: Florida in any season, on foot, rough terrain, wet ground (rain or swamp), mosquitoes, and snakes. And, unless this is a purely personal disaster, law enforcement is stretched too thin or has broken down, and there are packs of human trash on the prowl, so you would have to be careful, and probably hide at least part of the time.
Now add a child (or two or three) and/or infirm elderly people to care for into the mix. It seems to me that bugging out on foot would be (excuse me, this isn't personal) the stupidest thing I could possibly come up with.
As long as you're thinking about this, you might as well plan ahead. List all the possible problems you can imagine, from most likely to least-likely-but-who-knows. And decide the best way to handle them.
The two best plans would probably be to leave as soon as you know trouble is coming (with a definite place to go), or prepare to hunker down and ride it out. And you'd probably want to keep your options open, in case the situation changed drastically and you had to do the exact opposite of your initial plan.
Sue, imagining having to run with just a dog, 6 cats & 4 chickens.... Bleeech!