I use to tow a 6800# Wildwood with a '03 1500, 5.3, 3:73. I had the equal-i-zer hitch system. It did ok, little slow in places. Got around 10 mpg. I traded up to an '09 2500hd, 6.0, 3:73, and got 7-8 mpg. That truck pulled my trailer painlessly. I suspect that I got less mpg with the 2500 because my speed increased. The 1500 would do it but you had to drive it 24/7. The 2500 is just a hair short of setting the cruise and laying back. Personally I would not have gone any bigger with the 1500. Just too much trailer. It will wear you out. Especially with wind and trucks.
I know pull a 34' Sprinter 5th wheel w/ the 2500. And I'm getting better mileage. It pulls SO much easier than the bumper hitch. (sidenote sorry).
Good luck