September and October are the big months for hurricanes in Florida. Hurricanes feed off warm water and the warmer the water (like at this time of year), the stronger they are. Bookmark the NOAA/National Hurricane Center sites and keep an eye on their projected paths. Remember that they spin counter-clockwise and it's better to be on the SE side of them as they come ashore.
I was living in Orlando when Hurricane Charley and 2 others hit over a span of 6 weeks in 2004. Orlando was a hurricane magnet in 2004. I would not tempt fate and be anywhere close to a hurricane in any kind of an RV. I didn't much like riding out Charley in a house with no power and trees coming down everywhere. The destruction was truly incredible. The wind even blew down a long section of a 5 foot brick wall that surrounded our housing addition.
My .02 opinion - If in Florida, I would not travel northwards to get away from one unless you leave very early and you move several hundred miles north of the Florida border. If you get caught in it's path, and it is coming ashore on the Atlantic side, I would go SW. If coming ashore on the gulf side, I would go SE. Start with full fuel tanks and refill EARLY. Carry extra drinking water.