I wouldn't worry about the Tundra. Back when i was racing I bought a 26' enclosed Haulmark trailer (2 6k axles). When I bought it one of my friends was going to borrow a 1 ton from his work to pull it. When that fell through I used my Tundra. Not sure how much the trailer weighed but I'm guessing at least 3k. The car had to be 3200 without the driver and I had at least another 1000 worth of parts, tires, and tools.
Weight wise I was right at the max for the truck but anyone who has ever pulled an enclosed trailer on the highway knows they are a much harder pull than a flatbed trailer. The flat front of the trailer, 64 sq feet, is like a parachute. My Tundra pulled at 70 down the interstate with no problems for 200 miles round trip, 20 times a year, for 3 years. My Tundra is running great. After 130k miles I finally changed the tranny fluid and had it tested, not a single problem. That was with the 4.7 engine. The truck is a workhorse.