I have a 2500 with 5.7l hemi. It tows my 6000lb bumper pull just fine and even though its rated for 8500lbs I wouldn't go over 7000lbs partially because with the mega cab and 6.5 foot bed the truck is 6300lbs by itself and then I add 4 people, bikes, kayaks, firewood, cast iron cookwear and all the other food and gear needed maintain my rep as a chronic over packer. Stability wise you would probably be fine with 2500 but the gas engine is going to be working hard to move the weight your talking about especially if climbing is involved. Just my opinion.
2011 Ram 2500 Mega Cab 5.7L
2014 Rockwood Roo 25RS
Nights camped 2014 - 27, 2015 - 28
Nights camped so far 2016 - 26