PK:
Agree with all said so far. The Highlander is a great vehicle -- but it's not much of a tow vehicle. Toyota never intended it to be. It is essentially a Camry with a SUV body. The frame is essentially a uni-body Camry frame. As you no doubt already know -- this is one super comfortable vehicle when you travel on long trips. It is quiet and fairly fuel efficient. It's "4 wheel drive" setup is near flawless and works great in situations that the bulk of us "SUVer's" encounter -- normally snow, mud, and standing water on highways. It isn't much of an off-road, rock climbing, "conquer Killimanjaro" truck -- but again, that's not what or who it was designed for. It rides well because it's suspension is that of a car and not a truck. All those qualities make it an attractive "SUV" without all the ugly-SUV baggage. It is also why it's not very good for towing.
As everyone has already pointed out to you, the hitch weight (basically the downward force that the trailer will exert on your tow vehicle's hitch receiver) is the factor you need to worry about most. A TM (even the smallest 2619) when fully loaded (including propane in the tanks, maybe water, and all the "essentials"
will easily climb to 600 lbs or more. That weight will put you into the Class III requirement. COULD you tow with a lower class hitch? Well yes, but the real question is SHOULD you. You could tow with a hitch ball wired to the rear bumper with a coat hangar, but the real question is SHOULD you. The consideration is how safe do you want to be -- for you, your family, and anyone else on the road.
You'll also see a lot of discussion here about weight-distributing hitches versus weight carrying hitches. The W/D hitch basically has bars that act as cantilevers and allow you to transfer (or distribute, hence the name) the hitch load more evenly among the tow vehicles rear axle, front axle, and trailer axle. I know you've seen cars (usually a Ford Escort) going down the road with a U-Haul hitch bolted to the rear bumper pulling the largest U-Haul trailer that can be rented. If it's night time, the Escort's headlights are pointed at the top of the trees searching for owls because the butt end of the car is about .2 millimeters above the road surface. This is what a W/D hitch prevents. When properly adjusted, the longitudinal axes of both the towed trailer and tow vehicle are near level. I don't think you'll be able to use a W/D hitch with the Highlander because the hitch receiver will not be attached to the frame in such a way that the hitch can transfer the loads. This is because the Highlander is a uni-body construction and does not possess a beam type frame like you'll find on a truck. Because of the excellent design of the TM (already described to you), there are many folks on this site who only use a weight carrying hitch and have no problems. I won't "dis" any of them, but for me, a W/D is the only way to go for more added safety and piece of mind (I'm a suspenders and belt kind of guy anyway).
You're question is the first question that almost all of us asked when considering a TM for the first time. We all want reassurrance that the first thing we need NOT have to do when considering buying the TM is to also buy a new tow vehicle. If you are looking at a new TM & a new TV, you are looking at lightening your wallet to the tune of $50K (or more).
If you are a real Toyota fan, you really need to consider moving to at least a 4-Runner (if a SUV is your preference). A V-8 would be ideal; however, this year's 4-Runner went to a new V-6 and friends I know that have one are plenty happy with it as a TV. As you consider your decision, try to stay focused on a TV that is based on a truck frame with tow capacities no lower than 5000 lb, Type III hitch receiver, capable of using a W/D hitch, transmission cooler, heavy duty battery as towing minimums.
These are just my opinions, and there will be others on this site who will offer their's. The frequent contributers to this site are towing with (smallest TVs) 4-Runners, Sequias, Grand Cherekees, Tahoes, Explorers, Excursions, Durangos, Pilots, Odysseys, F-150s, Chevy 1500, Tundras as an example. Lots have bigger vehicles, and if you wander over to some of the other RV forums you'll get the RV "purist's" opinions that the minimum you need is a dual-wheeled, 10000 hp Cummins diesel, $3500 Blue Ox hitch, etc. Search this TM site and look at what real TM owners are using. You'll find lots of really good advice and help here. We all have our personal preferences but you'll notice most TM owners use vehicles that are at or above 5000lb/500lb hitch weights. I'll repeat myself -- the issue is safety. and when it comes to safety -- more is better.
Good luck and let us know what you decide. And if you have any other questions, this site is the place to come.
Ed