I live in Phoenix also, and have owned the same V6 4th Gen 4Runner you own. The poster who cautioned you on the hitch is correct -- that is a simple hitch simply bolted to the rear crossmember -- personally I would not tow anything heavier than a utility trailer with it, irregardless of what it is rated for. Crawl under and take a look at it and you will see what I mean. The V8 4Runner uses a proper frame hitch.
We sold that 4Runner and now own a 2008 4Runner with the 4.7L V8. And we tow almost exactly what you are contemplating -- a Rockwood 2109S -- 21' 8", Dry weight of 3624, GVWR of 4769. We drive up to the Mogollon Rim at 7700' for 4 day camping trips throughout the summer. I tell you that is the max weight I would tow with this vehicle, and I have the V8! If you try this with a V6 4Runner, you won't be happy and you will be trading in your 4Runner on something with a bigger engine in short order.
Also, if you put a Scan Gauge II on as I did, and program it to pull the trans temp, you won't be happy with the temps. Even with my V8, I didn't like the trans temps towing to the mountains. Mine came with an OEM trans cooler, albeit tiny (I believe that it also has a trans cooler inside the radiator). I changed the external trans cooler out for a larger trans cooler, and it lowered the temps quite a bit.
FWIW, my advice, based on where you live and what you told us you want to tow, don't do what you are contemplating. You won't be a happy camper.
I use a WDH with sway control and I experience no stability issues.