The car is basically 5 feet wide and 12-ish feet long. It weighs about 2250, and it will be no sweat for a dual axle skid-steer trailer. None. The total towed weight could be pushing 4000 pounds for the combination (if it's a beefy trailer) so you'd have to look at that number in relation to the towing capacity for your vehicle. If you have a larger truck, that weight should be in the ballpark of what it will handle, but you'll need brakes on the trailer. If not, this would be the point where you go down the list of people you've helped out in the past, looking for someone with a nice pickup truck or full-size SUV. Another way to do it is rent a car trailer from Penske, Ryder, UHaul, someone like that, and also rent the smallest truck they have to tow it with. (A small cube van will do fine.)
The tow dolly does require rolling rear wheels... or front wheels. Although I've never looked into legalities, there's no reason you couldn't tow with rear wheels up, and front wheels down. You would just need to secure the steering mechanism so that it doesn't allow the front wheels to pivot. I'd do this in two places-- one on the steering wheel and one on the undercarriage somewhere. But check the various state laws before you try this. You'll still need lights and a hitch, and most likely license plates if any part of the car touches the road. (That may be the killer right there.)
Good luck and be safe!
Ken