Truck should tow the load just fine, but you'll realize what garbage the U-Haul trailers are!
They aren’t all garbage if you do a proper pre-trip. Take a good air gauge with you, check all the lights, check the tires for tread/cracks/leaks, check the suspension, etc.
Be advised though, in the fine print, this is all on you and if something happens, too bad. Last time I rented one to pull home my Mustang GT, it was a disaster. Booked weeks ahead of time, ******* girl on the phone booked a trailer too narrow. (the car is a wide cow) They send me to another U-Haul that tried to send me out with a flat tire. And of course I can’t just swap a tire off another trailer they had there. They send me down the street to another UHaul and told me it was free. The place down the street gave me attitude and tried to send me out with two trailer tires 20 lbs low. I find out later that the brakes on the trailer were adjusted like shit and the surge brakes barely worked.
All in all, I hope U-Haul collectively gets a case of burning gonorrhea. The equipment can be ok, but they push it on people who generally have no clue what they’re doing. That’s the problem.