Concur, you have enough truck now for that camper.
My 2019 F150 supercrew 5.5' short bed 5.0 V8 standard tow package has a 1990# payload capacity and a 9100# tow rating. The current 5.0 has a LOT more power & torque compared to the 2008 4.6L. 395hp, 400 ft.lb torque vs. 298hp, 294 ft.lb. torque. 3.5L EcoBoost has 375hp, 470 ft.lb torque but it comes on at lower RPMs compared to the 5.0L V8.
The slightly longer 6' bed is needed if you are ever considering a 5th wheel. Also required with the Max Towing package or Heavy Duty Payload Package (HDPP). Both come with the 36 gallon gas tank and require the 3.5L EcoBoost. HDPP is required for truck campers.
Side note: The Ford 2008 Towing Guide is available online. I have a 2008 Explorer and downloaded it, I think, from Ford.com, to my iBooks.