Congrats! That first ride with a new RV is always exciting. I pulled with an older Suburban for several years and it served me well. Even with the 454, she struggled in the mountains. From what I've read, the power curve on the 5.3 and 6.0 is at a higher rpm range so don't hesitate to wind her up. Anticipate the hills, make a run for it and try not to back off unless necessary. Either that or just let her down shift and poke up the grades. The motor revving can be a bit un-nerving though.
Good luck with your new rig and have fun!