I pulled a 22' toy hauler with my F250 that weighed in around 11,500 lbs loaded. I had 1100-1250 lbs tongue weight and always tried to load tail heavy to under 11 percent (my receiver was rated at 12.5k/1250). You will want a weight distribution hitch just to negate any front axle unloading on the truck even if you are running a receiver that can handle that amount of tongue weight. I ran a single friction sway bar and 1200 lb L-bar WDH for seven years and over 70,000 towing miles with good results. Without the friction sway in place, it towed well even in steady side winds but wind guts required more correction than when I had it connected. My trailer was slightly shorter than yours but taller - I think the square footage of the walls would compare evenly and you will have the same experience.
