We pull our 3670 with a single rear wheel, 2WD Ram 3500. I'm pretty sure you'd be overweight with the 2500.
I didn't get the dual rear wheels as I drive the truck daily and find it easier to park than with the wider dually. If I was only using the truck to pull the trailer (and rarely needed to park in a parking lot) or if I towed every weekend, I might consider the dually, but you don't need it. The single rear wheel 3500 is rated to more than handle the 3670's pin weight plus is rated to pull the same 23,000 GCVW.
After all, the single rear wheel uses the same engine, trans, springs, etc. as the dually. The dual wheels do give you more payload capacity in the bed, but you already have enough with the one ton single wheel. Get the dually if you are okay with the extra width, plan on carrying more in the bed than the SRW is rated to when you aren't towing, and if don't mind buying more tires.
Thanksgiving week we pulled it over 3,000 miles (from Maryland to Kansas & back). No problems, no rocking.