I agree with what's been said, a small UHaul trailer should not be a problem. Your rig won't even know it's back there.
I'll emphasize that you need to carry an inexpensive pair of chains for the trailer as well, in case your plans happen to land you traveling during a storm.
On one trip, CalTrans turned me, my 4x4 truck, and my 1500lb boat and trailer away from Donner Summit during a heavy snow because I did not have at least one trailer wheel chained up. I had never heard of that before. I guess the chained up trailer tires act as a rudder, to keep the trailer from 'coming around' (jack knife) while the towing vehicle is slowing, on the ice.
1995 E350 7.3 Diesel, 4x4 high roof camper, UJOR 4" lift