I tow a 6200 lb 32' Rockwood that is about 7200lbs loaded for camping. Tundra tows it just great. Never any problem stopping or lack of power even in mountains going to Florida or passing. As long as you are within the specs on the Tundra it will do a great job towing the trailer. Toyota appears conservative on payload. My Tundra squats the same as my 2006 GM did with 300 lbs more weight in the box but technically 400lbs less payload. Not saying you should go over payload rating just pointing out that it appears Toyota does not push the ratings as close to the limit as others may. No facts just an observation on my part. In the end it's really about how comfortable you are with it.
