Is the max payload from the sales brochure, or from the sticker in the drivers door jamb? If from the sticker, should be a pretty good match as long as you don't load the truck bed full of stuff (firewood, coolers, etc) as payload would be your limiting factor (including truck cap on the bed if you have one). Also don't overload the trailer.
As for the hitch, you will probably be close to 1k lbs tongue weight (tw) once loaded up!
Also look into a hitch system with an integrated sway control. Equal-I-Zer 4 way or Reese Dual Cam (DC). I don't think I would rely on the trucks integrated sway control system, as that is more of a "reactive" compared to a proactive system like the Reese DC.
Other thing to keep in mind is LT tires compared to P rated tires! The soft sidewall can flex when towing, giving what I call a "wiggle feeling almost like a kid who can't stand still because he/she needs to use the restroom!"
Good luck!
