I regularly tow a 8.2k-8.5k lb trailer with my 14 Tundra Crewmax. I recently towed from Alabama to Kansas and averaged just over 9 MPG with some pretty serious hills and winds. Expect 8.5-10 MPG towing on average.
I'm cutting it close on payload and agree with the above poster about the soft suspension being jarring on a rough interstate with expansion joints.
On any regular road, it tows exceptional. The Tundra's 5.7L is a phenomenal towing engine. I've towed about 2k miles in the past year and for a gas engine you will have a hard time finding a better towing engine/transmission. Shifts to 3rd only on steep inclines.
I plan on adding either timbren's or airbags to address the expansion joint interstate problem. If I were buying a new Tundra again, I would definitely try to talk the dealer into getting some LT tires as well. The Bridgestone P rated duelers that come stock on some Tundras are truly terrible tires and wear extremely fast.
Make sure you check the payload of the actual truck you are going to buy and make sure fully loaded for camping your numbers are going to work out. That being said, your numbers look close as mine is ~1400lbs of payload on a crewmax 4wd. The 2wd double cab should net you a couple hundred more pounds.
Tundras are great trucks. You will have to look very hard to ever find a disgruntled owner for a good reason.