The U-Haul trailer weighs about 3,155 pounds. They will not rent it to you if you tell them you are going to tow a Challenger with it.
You only get the different axle and probably cooling too with towing package or Z71. According to uhaul the trailer is 2,210lbs so you're probably right near your towing capacity with a Challenger on it.
@swathdiver quoted the trailer weight of the Flatbed Utility Trailer that was linked. There is a smaller Auto Transport that weighs 1K less than the one @ReaperHWK indicated.
Here's what the Auto Transport looks like:
Two very different trailers.