I pulled a similar trailer to yours out to Yellowstone with my old half-ton Suburban. If I were you, I'd also install a new diff cover with cooling fins. IMHO the rear axle is the most worrisome component of the powertrain, My friend now owns my Suburban, it has 250k miles on the original engine and transmission, but it's on rear axle number 4. I broke it twice while on vacation pulling my trailer. The third replacement was because of improper break-in, under warranty. I'd already lost 4 days off my vacation; I didn't want to waste another day putting 500 unloaded miles on the axle before I started towing.
I'd also make sure I packed one of those infrared thermometers, to check the rear axle temperature during the trip. We actually did some traveling at night, so we wouldn't be fighting 100°+ temperatures, to help the axle.
