With the biggest rental truck, 8-10 mpg is probably a good estimate. I bet the car will cost, at most, a couple of mpg, low end if it is flat and more if mountainous. Doing the arithmetic with a 30 mpg car and 2 mpg loss (8 down from 10); you will only save about $45 in fuel. A dolly or transporter will cost, you tell me, $150? Fix my calculations if necessary. Money wise, cheaper to drive both unless you add in wear and tear on the car. It will probably be an advantage to have the person that would otherwise be driving the car in the cab with you. OTOH, maybe not. The other possible down side is you can get a lot of stuff thrown onto the car and get stone chips. Have you ever followed a truck at 5 feet for 1300 miles?
I would get a dual wheel trailer rather than a dolly. You can back it up. You can see the wheels of the trailer in the truck mirrors. (With a dolly you can have a flat and ruin a tire and a wheel, heck, you can lose the whole dolly and car and not notice if you have a big truck.) You will save some wear on your vehicle over a dolly. You will have another set of brakes making it safer.
I towed for 2100, 2400, 700, 670 and 300 miles. It would cost me the difference between the dolly and transporter in Rolaids.
It has been about six years since my last rental. I found that you can bargain with the companies, especially with the mileage and days if not the price. Call everyone and then call back the company you want to rent from and tell them what the other guys are quoting you.
I have had good (fast) trucks and real (slow) dogs. I wish I could say how to avoid the dogs, but I can't. Fortunately the slowest one I only had for 670 miles.