GM tow ratings for 2011+ 2500HDs vary a lot. From about 9500 pounds to over 14k pounds. 4.10 axle makes a big jump, much more than the 10% gearing difference compared to GCWR difference of 16k to 20k. So check your RPO sticker in glove box to confirm GT4 or GT5 for 3.73 or 4.10 axle.
9000 pounds for a 5er should be just fine for either. Use tow haul mode, and M5. Expect some downshifts to 4th or 3rd gears on the hills. Let that engine as peak torque is in the 4200rpm range. My 6.0L wakes up over 3000rpm and pulsl hard to over 5500rpm.
A & A parents of DD 2005, DS1 2007, DS2 2009
2011 Suburban 2500 6.0L 3.73 pulling 2011 Heartland North Trail 28BRS
2017 Subaru Outback 3.6R
2x 2023 Chevrolet Bolt EUV (Gray and Black Twins)