Small utility trailers are a dime a dozen. How 'bout just buying a used one then selling it at the destination. It'd probably be cheaper anyway, and you won't have to rush to keep the number of days down.
U-Haul locations are usually distributors - prices and policies differ location to location.
They wouldn't rent me a car hauler to put behind my motorhome one day - they said I had to rent their truck with it.
But right down the street an other location had no problem with renting just the trailer - and at about 1/2 the price of just the trailer at the first place!
Check several - also don't forget to call the U'Haul 800 number - often they are cheaper than over the counter locations.
I was renting a truck one time - a location told me a price for 1 day. The 800 number quoted a price for 2 days that was less than the location quoted for 1.
Then they told me to pick it up AT THAT SAME LOCATION! The guy was pi-- - but so what!