For the Tundra, the 31QBTS is a long trailer. I have the 11' Tundra Crew Max Limited pulling ~8k fully loaded 29' TT. Pulling that much weight, as many say, is slow going in 3rd gear up the steep hills. But that's OK because on the flat road 65mph is easy in 5th gear. I echo the comments about the thirsty engine - I carry a 5-gal fuel jug in the back just in case.
Trailer sway gets to be a problem with long trailers. Industry accepted practice is to match the TT length to the TV wheelbase. Crewmax has 145" wheelbase, translating to a recomended max TT length of 29'. Under most any condition, 29' is considered the maximum. Since your TT is longer, the recomended adjustments are:
Use a weight distribution hitch that transfers the articulation point forward such Hensley or Pullrite
Correct weight on hitch ball (very important)
Sway bar on TV (Toyota makes a nice one)
Other things that help control sway (after it has started) seem to be standard on these recent fully equiped Tundras such as VSC and TRAC.