When my daughter moved from AZ to WI for College I towed her Jeep Wrangler behind my 2016 GMC Sierra 2500 HD Duramax.
When the kid at the UHaul dealership entered the information into the computer he told me the 2500 was not rated to tow a car hauler trailer....
He had selected the wrong tow vehicle in the software.
The UHaul trailers use surge brakes instead of electric brakes, if I was repeating a long-distance haul I would rent a trailer from somewhere that has them available.
I would think you will be fine with your 1500 unless the tongue weight and cargo in your truck go over the weight capacity of your truck (not that I haven't exceeded that when I was in my youth but ignorance was bliss).