The RV you mention has a GVWR of 20,000#. If fully loaded you will be pushing 30,000# combined. Most likely will not NEED bags but a set of Bilstien's and bags set to 30# with RV attached will make for an even better ride.
Your trucks GCVWR is 27,300# with 3.73's. If you had 4.10's it would increase to 30,300#. Best thing is to tow it and decide if the gears need to be changed. Not the PERFECT gearing but I see ZERO issues.
I towed a combined 29K with a 11 HO RAM with 3.42's, only issue was getting the load rolling on a grade. Towed in 5th with same rpm as 4.10 in 6th. Your 16 is physically more capable than my 11 was.
Buy the rV hook up and see what you think. I am betting you will be very happy.