Just as a point of reference, I have a 2002 Yukon XL with the 5.3 and 3.73 gears. Tow rating is 7700 lb. GVWR is 7000 lbs and combined is 13000. I tow a 2008 Jayco 29BHS. Max weight for the trailer is 7500 lbs. So yes, I am pushing the envelope (but haven't weighed anything). I had the vehicle before the trailer and drive it often, so that is why I use it as a TV. Pickup truck will not work for my situation.
My experience has been good. I typically don't go more than 200 miles on a trip (one way) but in my area there are mountains to deal with and whatnot. I feel quite confident with my setup and on the road I am fairly relaxed. I feel the push/pull from box trucks the most, not so much big rigs, surprisingly. I use an Andersen Hitch and am pleased with it. I did upgrade the hitch to a Curt, because the OEM GM hitch could have problems.
If I were doing more than weekend things over longer distances, I would probably want a beefier TV, but mainly because at that point wear and tear on the 1500 would begin to be a concern. For my relatively occasional use I have no qualms about going anywhere.
One thing I did learn was to go downhill in a lower gear, like 2nd instead of 3rd. I went down from a campground at 7000 feet (Big Bear, CA) and got the rear brakes rather heated by the bottom despite judicious use of the brakes and low speed. There is a lot of weight on the back and the rear axle is doing more work while towing and braking than usual. Since the rear brakes are smaller than the front, they were not quite enough to stay cool. That issue would perhaps be lessened with a 2500, depending. I think it was more my gear selection than anything.
Just food for thought. My opinion is that you would be okay with a 1500 and your trailer.