Here's where I'm at on this deal.
My dad towed a 7,000lb TT twice to Alaska with a 69 Chevy half ton. This truck had a 12 bolt with 3.73 gears, a 350 and a turbo 400 and drum brakes all the way around. He also did 10's of thousands of miles across the US with the same combo. He also had a cap on the truck that weighed about 300lbs or so and a 15' aluminum Gregor on top of that which weighed about the same. He also loaded the bed with a 50lb+ outboard motor, tackle, poles and a freezer....yes a freezer to keep the fish he caught up there!
The truck you has about twice the power if not more. It has a WaaaaaaaaaaaaaaaaaaaY better engine, a Waaaaaaaaaaaaaaaaaay better tranny and the brakes aren't even in the same universe as the 4 wheel drums he and I had.
I also towed a car trailer with a 3,200 lb race car on it with this truck for many, many years. Never a problem with handling or any other problem.
The bottom line for me is your truck is light years and then some ahead of the truck I had up to a few years ago. It is FAR superior in every single category.
I would tow a 7,000 lb trailer with your truck in a heart beat no matter what that little mylar sticker on the door says.
But that's just me. If you feel you need a class 4 truck to pull a 7,000, lb TT like some on this board do; buy one. Better yet, buy a class 8 truck because you never know when your going to move up in trailer size. :B