You will be just fine. Take it easy going up and down the mountains. Go down the mountain in the same gear you go up in. Use your engine instead of your brakes. That diesel will be your best friend going down the mountain. When you do use your brakes, do a quick 10 mph deceleration and then let off the brakes, use the engine to keep your speed down.
My fiver weighs 12,300 lb loaded, I have a duramax 3500 SRW and no issues going from NC to IN. Been up and down some long 7% grades without even a little issue. Slow and easy, you will be fine.
2014 Crew Cab Chevy Silverado 3500 4wd Duramax/Allison
2014 Sabre 34REQS-6