I just traded a 2005 GMC that had the 6.0 liter and 4.10 gears. The towing capacity was 8100 pounds. That should be more than enough for your camper. I towed two different 31' TT with it over six years and 90,000 miles. It never left me stranded although there were some repairs along the way. Fuel economy was 7.5-8.5 towing and 15.5-16.5 empty. 60-65 mph was the sweet spot for power and fuel economy. I traded when I found a great deal on a 2500 with the Duramax to allow for future upgrades of the TT otherwise I would still be driving it.
