I agree with downtheroad's post above. You could possibly improve the ride a bit if all the setup details were perfectly setup, but with that amount of weight/load, then you may still have a rough ride regardless due to the capacity of the truck.
I pulled a ~6k loaded TT with a Silverado 1500 for a lot of years. The WDH was set up well, and when I switched the stock P tires to LT load range D, I noticed a lot of improvement and it did just fine, but it was still night and day when we finally upgraded the truck to a 2500.
If you decide to stick with the 1500, check out the points DTR listed, (particularly the WDH setup). Otherwise, I'd say a 3/4 ton truck would definitely be a step in the right direction.
IMHO, although a long bed is always recommended for stability over a short bed, the "standard" (6.6') bed Chevy's do fine, especially with the added length of the quad/crew cabs. My 1500 was a standard bed quad cab and the 2500 is a standard bed crew cab
Best of luck.
PS - my DW was against upgrading the truck too. She didn't understand why if the 1/2 ton did the job fine. After we upgraded she finally understood. And frankly, there's a safety factor as well.