I can't believe that truck would not safely tow that trailer.
I have almost the identical setup, accept my RAM is a SLT 2-door 2wd w/8' bed.
Towing a ML23FB, pretty much the same weight as the trailer you are looking at.
The 4.7 is not the strongest of motors but in the tow/haul mode I still have plenty of power available.
The Micro Lite series trailers were designed to be towed by mid size SUV's.
I even have a double wall utility cap on my truck that probably brings my 1700lb payload capacity down to what your truck is rated at.