My 2008 Highlander (with factory tow prep package) towed trailers for 140,000 of the 185K miles I put on its odometer. Cargo trailers in the 6x12 size with weight up to 3500 lbs, a 17' Burro, and a 16' KZ E14RB. It did very well, the 3.5L had plenty of power.
You probably will not load that TT much more than 3600-3800 lbs if you're halfway careful about it. You will be traveling with a family, I assume, which is more weight in your HL than mine (I traveled alone). Even so, I would not hesitate to use the trailer you're looking at, except for one important thing: the hitch weight of 370 lbs. I'll bet that is dry, without the LP tanks or battery in place. Real world, you may have a difficult time keeping that hitch weight under 500 lbs once you load up. Not impossible to do, but you'd want to get a Sherline scale and check it before you left on any trip to make sure you're not overdoing it. And if you wanted to use a weight distributing hitch, well, they're another 70-95 lbs, so it'd be over for sure.
