if the 1500 factory shocks are anything like 2500 factory shocks, they are NOT anywhere near optimal for towing or loaded riding, more for unloaded, even then marginal. On my 04.5 2500HD I replaced the factory shocks with bilsteins at 10K miles, on the 2015.5 at 500 miles. the difference in ride, loaded and unloaded and towing was very noticeable. Especially towing the compression and rebound damping on the bilsteins is much more controlled giving a much better ride.
Now that said, our 2500's tow a 9000lb trailer with 1500lbs on the tongue. with 3 people and stuff in the bed and the trailer hooked up, I go over the scales at 10,000 on the 2015.5 on the truck. right at GVWR. the 2004 scaled and 9700, 100 over the 9600GVWR.
First, make sure your WD hitch is adjusted properly. and IMHO the trailer size is very marginal for a 1500.