The Tundra is capable to tow that trailer but you will be over payload for sure. The bigger question would be can you keep it under the tire and axle ratings?
I towed a tt of similar weights with my old '07 crewmax. Loaded up we were 7600lbs with 950lbs of tongue weight. With the wife and two boys on board we were 400lbs over payload. I was able to keep it under the axle rating and the upgraded E range tires. It towed great but I was never a fan of pushing limits or having to watch what I packed, plus the kids weren't going to get any lighter. I now have a 3/4 ton truck. (Still miss that Tundra) I have no doubt that the Tundra could tow that tt safely but I think you would be more comfortable with something a little smaller/lighter.