After reading these responses I'm beginning to think there is something wrong with my truck. I have the same truck as the OP but a 2014. I wouldn't say it would tow that with no issues. My 31' tt only weighs 7600lbs loaded and my Ram doesn't pull as well as my old Tundra did. I wouldn't even consider pulling 10K+ with mine.
The issue I have isn't power, rather the 3.73 gearing and the transmission ratios and programming. Mainly 1st and 2nd gear. The flats are ok but always in 4th gear and a lot in 3rd with a slight headwind. I know it needs to rev and I'm not afraid to do so but my old Tundra would hold 5th all day long with the same tt.
Hill starts from 1st gear is where it struggles. It pulls hard in 1st up to redline but dies in the shift to 2nd. The drop in RPM is huge and falls well below the power band so it bogs down and can't accelerate. If you're at speed (above 3rd gear) or have a running start you may be ok.
A number of times I've had to manually hold it in 1st and crawl for miles at redline holding up traffic. The first time it happened scared the **** out of me and became a dangerous situation. I was used to towing with the Tundra and easily accelerating up hills so I expected similar or better performance from the new Ram. I was stopped at a light at the base of a long, fairly steep hill in northern New York behind a semi truck and a growing line of traffic behind me. The semi topped out at 20mph which was killing me. The road was clear ahead as far as the eye could see so I signalled, stepped on it, and pulled out to pass. All was good until we got beside the semi and it shifted to 2nd. My truck bogged down and slowed. I shifted manually back to first and it held speed but was redlined and couldn't outpace the semi. Of course the traffic behind me had closed the gap and I was now stuck in the oncoming traffic lane. No choice but to slow and let all the traffic pass so I could pull back in. It was an eye opener. I brought the truck back to Ram to have it checked out and they said it was normal. Highly disappointing.