I have a 2015 1500 4wd with the 5.7 + 65RFE transmission and 3.55 gears, have towed ~7200lb (2 axle, surge brakes) interstate a couple times and ~3500lb (single axle, electric brakes) cross country with a few hundred pounds in the bed. Compared to your powertrain my 2015 has the electric power steering (no PS pump) and supposedly 5 more horsepower and a newer generation of engine/trans controller but should be more alike than different. My tire size is 285/70R17 (33" diameter) and I have calibrated the truck for that tire size using JSCAN. No engine modifications or tuners or performance parts. While towing I use the "Tow/Haul" setting, though I've forgotten to switch it on a few times as it turns itself off at each restart.
No trouble to report. The truck manages that amount of weight confidently, braking and acceleration and steering command feel well within the truck's capabilities. Transmission doesn't seem to have any difficulty on hills even in the southwest during summer. Highway fuel mileage while towing is pretty awful, even in California where any trailer means 55mph (I have no interest in collecting citations and paying more for insurance) best I've managed while towing a trailer is ~13mpg and more often it's 11.
While the MPG sucks it's nice that it never seems to struggle on highway grades to sustain the speed limit. Even heading up the rim from Phoenix toward Flagstaff loaded I can stay in the left lane without holding anyone up and without feeling like the engine's struggling or flying apart. Never seen any cause for worry on the temperature gauges, engine or trans. Oil temperature creeps into the 220's on severe grades when engine RPM's up, but it levels out and comes back down fast when the hard work is done.
In other words for the ~6k dry weight on your trailer, plus all your bags and consumables you should be in good shape. I trust you got all your bases covered on the normal maintenance and safety responsibilities, no need to go over that. Your biggest enemy is going to be tongue weight the 1500 doesn't have a lot of capacity for that.
For what it's worth I've got the factory trailer brake controller, it works smoothly and it's nice to have it integrated instead of an extra wart in the cab like my old work truck's aftermarket brake controller. If you don't have a brake controller yet that one's got my endorsement.