Omrod
GMs last 1500HD was in '06. It came with a 6.0 engine 8600 gvwr 6000 rawr and basically the old 3/4 ton chassis.
For later 1500 GMs like your 2015 1500 GM has the NHT package which upgrades gvwr to around 7xxx lbs.... 4300 rawr.
Anywayz you won't have any issues pulling a small lite weight bumper pull TT without a WD hitch. Pump the trucks P tires to max sidewall pressures. Your stressing needlessly.
I use the wifes 2016 1500 chevy 5.3 engine 6 speed tranny pulling a 10k car hauler with a 6820 lb tractor/cab 11' 8" on the deck and had no sway issues.
I did add a WD hitch for sag issues with 1280 lbs on the bumper which caused a 220 lb front axle loss (steering).