I pulled my 5500 pound dry TT for 2 seasons with a 2003 F-150 Supercrew 5.4L/3.73. You have two gear to accelerate and one to cruise. Expect speed to drop on hills and downshifts to 2nd/4000rpm at 55mph. If you can accept that, the truck will be fine. I'll assume you are just traveling with 2 people since you are looking at rear living rooms models. You should have plenty of suspension to handle 850 pounds of loaded TW, two people, and a bed full of camping gear.
Get a WDH with integrated sway control and learn how to adjust it. Get a proportional brake controller. Turn off overdrive. Skip the air bags.