A supercab shorty has a wheelbase of 142", or about 12'. It has a 3' front overhang for a total of 15' from the nose to the center of the rear tires. Therefore you need a minimum of a 16' trailer to haul it safely.
A 16' flat bed utility trailer would do the job, but only if it has enough GVWR to haul the weight of the truck. The common light-duty 5,000 or even 6,000 GVWR trailer would probably be overloaded, so I'd want one with at least 7,000 GVWR (two 3,500 pound axles) to haul that empty pickup.
The standard U-Haul car hauler trailer:
Originally Posted by U-Haul
Towed vehicle requirements:
Must not weigh in excess of 5,290 lbs.
Must have a maximum wheelbase (distance from front axle to rear axle, usually posted on the driver's side door jamb) of 133 inches.
So the wheelbase requirement eliminates the standard U-Haul car hauler trailer. Penske car-hauler trailers are even more restrictive. Ryder doesn't rent trailers other than for the big trucks.
Big-Tex and other trailer manufactures make car hauler and equipment trailers that can haul an 8,000 pound Superduty dually with 173" wheelbase, but you probably won't find them at the local trailer rental store such as U-Haul.
I would let my fingers do the walking and find a local equipment rental store, and ask about renting an "equipment" trailer that will handle the pickup. Lots of equipment trailers are intended to haul tractors, backhoes, etc, and would work for hauling a pickup.