Start off by determining your cargo carrying capacity for the truck. Should be on the sticker on the door jam. With a 7000 GVW trailer, your tongue weight will be somewhere in the 900 to 1000lb range.
Take the number off the sticker on the door. Subtract 900 (best case tongue weight), the remaining balance is what weight is remaining for you, your passengers, any cargo, fuel weight (8lbs per gallon), and weight of your WD hitch (75-100 lbs). You may find out that you exceed your cargo carrying capacity.
After that, it's your judgement on what you want to do. Some folks focus on RAWR (Rear Axle Weight Rating), instead of the GVWR of the truck (which is curb weight plus cargo capacity). Some swear by not exceeding the GVWR of the truck. I won't pass on my personal belief, but I think there's room for both, depending on the situation, and how much weight we are really talking about.
One other consideration is the wheel base of the tow vehicle. I don't know what the wheel base of the Avalanche, but with a 29 ft trailer, you could run into issues. Someone I know recently tried to tow his 26ft (I believe) TT with his Jeep Grand Cherokee as a test, and he decide real quick the Grand Cherokee wheel base was too short. He has a 3/4 ton truck but just wanted to know if he could tow it with the jeep, and decided he could not.
Hope it helps
Mike