1-way rental for car dolly is probably 4-figure as well.
Don't you have significant other that can drive the car?
By the time you get bracket, lights and brakes, it will get cheaper to ship it.
Or sell it locally and than buy another one at destination.
On other hand - people have been pulling toads with no brakes for decades.
2400lb no brakes car behind 12,000 TC unit is not that big deal.
When I was trailer-shopping in Nebraska - local dealer offered me new 7k equipment hauler with no brakes. That was years ago, so I wonder if the law have changed.