I had a 25' Carson Toyhauler that I used to to with an 89 Chevy 350 K2500. Roughly the same weight as what you are considering. Your modern engine produces about 50% more HP and Torque than my old chevy.
I towed mostly in the mountain west, and the trailer broke the truck - specifically the transmission. The 700R4 was not a very good transmission for towing.
I had to use a weight distributing hitch with big bars, especially when hauling empty. Toyhaulers have very high tongue weights, loads behind the rear axle will help. Its unlikely you'll get a toyhauler unbalanced unless you have a load in and all the tanks are empty. I used a weight distributing hitch with a built in cam-type anti sway feature. Never had an issue with the mechanics of towing the vehicle after that.
Gas mileage was pretty abysmal - below 7 towing, so check your tank size to see what kind of range you will get. I got used to hauling a 5 gallon jug of fuel with me just in case.
That trailer is going to be close to the Toyota's limits, and in my experience that can lead to a less than enjoyable driving experience.
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'99 Beaver Monterey 30', Cat 3126/300
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