What year? Im currently running an 04 duramax 4 door shortbed and a pro trak gooseneck trailer. Truck and trailer with me in it weighs 13140 empty.
I have owned 3 dodges. a 92 5 speed (stock then hopped up) an 01.5 auto very mildly worked on, then an 01 6 speed extended cab. All had 3.54 gears and that hurt them a little towing but helped as far as fuel mileage. In 03 or 04 they went to the g56 tranny over the nv5600. The nv5600 can have more problems than more people think and are expensive to work on.
If you are towing real heavy id get an 04/05 with 4.10 gears and 6 speed. I dont think new auto (7 speed tranny) came out till a year or two ago in select trucks. Then put a set of gauges in it and a edge box.
How much weight do you put behind the truck normally?