I have a 2001 Tundra 4x4 and I've been towing a 26' Outback travel trailer since October of 2003. "Scaled" weight of the trailer in camping trim (no water on board) is 5,600 lbs. I have a tranny temp gauge mounted to the 'A' pillar with the sending unit mounted in the tranny pan. I always tow with OD turned off unless I'm heading down a long mild grade with minimal throttle. While having nothing else to do while towing on a long flat section of Interstate 5 here in northern CA, I turned the OD on. I was cruising along @ 60 mph and the tranny temp gauge was reading approximately 180 degrees. This was on a summers day with outside air temp around 95 degrees. After a few minutes I observed the tranny temp climbing. Once it hit 200 degrees, I turned OD off and about 5 minutes later it was back to 180 degrees. It showed me the tranny was definitely working harder. I'm running Amsoil in the tranny with a larger aftermarket cooler and an in-line filter. I now have 126,000 miles on the odometer and we've towed to southern CA, the coast of northern CA, Oregon, Nevada, Idaho and Wyoming with not a lick of trouble.
Your trailer is about 2,000 lbs lighter, but even so, I would suggest leaving OD off unless you are heading downhill. Your tranny will appreciate it! If you're curious, it may be worth it to you to install a tranny temp gauge and see for yourself how the tranny temps fluctuate under load.
Happy camping!