Love the mindset of 90% of the responders. YES, a properly set up 2011/2012 1500 will tow your rig with ease and give you the non towing ride and fuel economy you are talking about. We live in the western mountains of Idaho and the ranch trailer I tow weighs in around 10k when loaded, so I do have a little experience with the subject. I bought a 2011 1500 GM NHT max tow, as I did not like the 3/4t and 1t trucks we have for the ranch use. I have NO problems with the set up and the built in braking system when in T/H mode works outstanding.
Do NOT listen to the folks that say you need a semi tractor to tow your trailer, cause it ain't so. Would it do a better job, sure, but at what expense. I'll take my 1500 NHT max tow, towing 10k any day over a harsh riding 3/4t gas hog, which the 6.0 is.