I have a 2015.. don't think there are many changes, 3.93 gearin, 32gallon tank, 8spd auto. 10,200# towing capacity.
The payload is your limiting factor, mine is 4wd 4 door (not the crew cab, the slightly smaller) 6' bed. Payload is a shade over 1300#. With a 6000# TT you'll likely have 700-800# tongue weight.. and 100# or so of WD hitch. With my specific truck that'd leave around 500# for me, my wife, our stuff, firewood, water, etc.....
If you're okay risking going over the payload, or pack really light might be fine. The engine is strong, and the 8spd makes for some nice towing.
Personally for a TT that big, I'd go with a 3/4 ton.. and if you travel a lot.. diesel.
2015 RAM 1500 4x4 5.7, 3.93
2013 Econ 16RB TT