I plan on towing a 35 ft 5800 pound travel trailer with my 2006 LT Suburban that has 100,000 miles on it.
The pull will be 2000 miles from Ohio to California, Trailer has a 600 pound dry hitch weight with trailer brakes, both Suburban and trailer will be completely empty, I will be using a 800 pound dry hitch and 10000 pound weight distribution hitch with sway bar. anyone towed this far with 2006 suburban with 100,000 miles? any thoughts? Can this hurt the tranny?

 

I'm assuming you're talking about a half-ton Burb? If it's a 3/4 ton, then it's a no-brainer.

I've towed the same sized trailer with my '01 half ton, and we took it out to Yellowstone That was over 5000 miles of towing over 2.5 weeks. At the time, the odometer was around 140,000. We took other trips, totaling 15-20,000 miles of towing total. All of this was done after the odometer turned 100,000.

Couple of things I can offer:

1) The weak point is the rear axle, not the transmission. My truck has 190,000 miles and it's the original transmission, and it still operates flawlessly. It is, however, on its third rear end. Broke it several times while towing.
2) Tow in third gear - it's a 1:1 ratio, and puts the least stress on the transmission.
3) You're going to be going very slowly up the hills when you get into the Rockies. Stay on the interstates to avoid the really high altitudes. At 9600 feet, the best the truck could do was 25 MPH in first gear. You'll be chugging slowly towards the Eisenhower tunnel on I-70, or whatever highway you choose to cross the Divide.
4) Pay attention to the temperature of the rear axle, especially on hot days or days where you're driving 400 miles or more. I was actually crawling under the truck and putting my hand on the axle. If it's too hot to touch, take a break of a few hours and let it cool down. We actually did some overnight driving, when temperatures were cooler.

Obligatory pic at the 9600'-foot pass in Wyoming: