I think it'll tow it pretty well. The chassis is does really well for towing. The engine is the weak link for sure. But a car on trailer has far less drag than a travel trailer. So it'll pull a lot easier despite being a bit heavier than some travel trailers.
I would also recommend rear air springs. They both help support the load and keep the vehicle leveled up, but also increase effective spring rates make for a much more confident towing experience. You'll have a lot less wallowing and body roll with the air springs with that extra weight on the rear axle.
All 5th gen 4Runners have the same tow setup, so there's no tow prep package to have or not have. The only issue that seems to come up is transmission temps. I don't think you'll need one if you aren't going over any big passes regularly. But it may be worth adding an OBD2 dongle with the Torque app or similar to watch your trans temps in real time and make sure it's not getting too hot. The ELM327 bluetooth transmitter and the app cost less than $20 combined, so it can give you some piece of mind if you're worried about it.
Uhaul trailers kinda suck. They're really heavy and usually have surge brakes that aren't very good. If you can rent a normal flatbed car hauler with trailer brakes it'll be a lot better experience. And it'll probably be half the weight of the uhaul trailer.
I would not install a trailer brake controller. I have one hardwired in my 4R, but have since used a Curt Echo wireless inline brake controller. No install needed. Works great on almost anything with a 7 pin plug except on some Ford trucks that use non-standard 7 pin electronics. Plus you can take it with you when you change vehicles.
Good luck towing your car.
Also - just for fun. I took this pic in Texas. On the highway. So who says a 4R can't tow? This bad boy is double towing!!