Congratulations on your new truck.
Did it come with a manual?
Most vehicles have a limit of what can be carried on the ball without a WDH. I've usually seen these at 5,000 lbs and 600lb TW.
But some HD used to have higher limits (7,500lb trailer/1,000lb TW) without the WDH. ( IIRC)
I haven't researched trucks in a few years so maybe your 2011 2500 has no limits. The manual will tell you.
Here's a Chevy towing guide
that might help.
As for sway control, I am not convinced that the built-in sway control (using truck brakes and reducing engine power) that come with these trucks are as effective as a good WDH with sway control.