I use to own the same truck. It will definitely do the job, however, if memory serves me correctly you won't be "legal". I believe that the quad cab 4x4 with 3.73 was rated at either 9400 lbs or 10,400 depending on the package with a gcwr of either 17k or 18k again depending on your vehicle package. Your moving to a fifth wheel that weighs empty at 14k and realistically loaded at over 16k. Your truck empty weighs over 7k so legally your well over your "legal" limit.
Changing to 4.10 gears won't help with the legal weight issues and won't match your tranny programming. Even with the 4.10 from the factory, max towing was 12,400 with a gcwr of 20k. Your over that with the 3.73 or even the 4.10. I'm not suggesting to not keep your truck, just that the numbers are problematic. It has only been in the last few years that the big towing numbers have come out.
That 5.9 is a great engine, but to upgrade your power put a tuner on the truck and a bigger exhaust. To me that would be better all around than changing the rear end.
Best of luck and enjoy you're new unit.
2013 Ram Longhorn 3500 Crew Cab 6.7 Turbo Diesel, Aisin Transmission.
2014 Jayco Eagle Premier 351 RSTS, Mor/Ryde Suspension and Pin Box, 17.5" wheel upgrade, 18k Pull Rite hitch.