I basically have the exact same truck and about the same weight trailer (ours weighs 7,030 lbs. loaded) and have not had any issues what so ever in our 15,000 miles of traveling. My only advice would be to add an additional transmission cooler just to aid in keeping the tranny cool. I assume you have a 4L60E transmission which is actually a great transmission which tows great with very little searching. It will be a little sluggish on really steep grades but just take your time and it will do just fine. We have towed through the Rockies and Smokies with little to no issues what so ever. A good weight distribution hitch and sway controls are a must though for safety.
