If you load the fifth wheel to 15.5K, the pin will likely weigh around 3,500 lbs. That should be within the capabilities of a single rear wheel F350, but I would weigh the truck with full fuel, hitch (or add weight if you don't have the hitch) and occupants to know for sure. The rear axle numbers are what matter the most.
What Todd said on length; since the front of the fifth wheel overhangs the truck bed, you're not increasing the overall length all that much - especially if you consider that 3 - 4 feet of the pull-behind's length is the A-frame tongue on the front of the trailer. A good fifth wheel pulls better and is more stable than even a well-setup pull-behind. We started out with a 6.5' bed and an Andersen Ultimate hitch (non-sliding hitch). I could get the truck and trailer to about 80 - 85 degrees backing up. It was never an issue getting into or out of an RV site. Of course, with an 8' bed, now, that's not an issue at all.
Rob