Well, as is often the case, I am going to play devils advocate here to some of the other comments.
First regarding the youtube video of the GMC truck pulling the trailer, I saw nothing there that indicated to me he would have to be over stressing the truck. He was running it a lot harder than most people would anyway....80 mph ? Most of us do not run that hard, and there is really is no "need" to rev it out to 5500 rpm. But even if you do, that is likely not "hurting" it in the overall sense, as the engine only spends a few seconds at a time there. Yes, if you had to run it near redline constantly to get the job done, that would be different, but from what we saw there, it could easily run at normal tow operation with probably no more than 3500 to 4500 rpm. That's nothing at all to a small block gas engine. It looked the trans temp stayed reasonable as well, but I do agree a large, quality trans fluid cooler would be a good addition.
Regarding changing the rear end to lower gears, yes actually, that sometimes is the only difference made when the factory states a different tow or load capacity. For instance, our '06 diesel dually has 4.10 gears, and a GCWR of 23,500 pounds. If it was fitted with 4.30 gears, the GCWR goes up to 26,000, with no other changes.
To the OP, is your truck 4WD ? If so, changing the gears in both the front and rear is going to be fairly costly.
As to whether your truck will be a good match for whatever trailer you want to pull, as is almost always the case with the lighter duty trucks, the first limit you run up against is payload (GVWR) or rear axle weight capacity (GAWR) of the truck.
Good luck with your choices, and have fun picking out a trailer.