I have the same truck in the '03 model. Mine is the 6 spd manual 3.73 axle 2wd quad cab short bed.
Dodge gives us a 13000-13250 lb tow rating.
Dodge gives the 2500 a 6010 RAWR that will be carrying all the weight in the bed.
My 2500 rear axles scales ar 2820 lb leaving it with a 3190 lb in the bed payload.
Your 4wd may have 50-75 lbs more on the rear axle.
Best to drop by the scales and weigh the trucks front and rear axles separately. That way you will know how much load your left to play with.
A single gross weight is as worthless as titz on a boar hog as it doesn't tell you if a tire/wheel/suspension is overloaded.
And of course the Cummins sure won't have any issues towing a 13k lb trailer. Your gonna' love it.