The back of the trailer is going to have more movement then over the axle which could cause motion sickness. In the midwest heat would be a concern where your at should not be as much of a issue. My Collies always rode in the truck cab so don't have much experience. I know my trailer is very warm when coming off a long highway drive.
I did try hauling them one time in the topper of the camper and one got extremely sick for several days. I had the camper windows open and wonder if Carbon monoxide might of got in. After the trip I sold the single cab and bought a crew cab truck.