heavy trailer with brakes or lighter trailer without?

In a couple weeks I will be towing my wifes car (Toyota Celica) 1100 miles across the country and I need some advice on which trailer setup is best. My 04 Grand Cherokee has the 4.7L V8 but it did not come from the factory with the tow package. I've installed a hitch and wiring harness and used it to tow lighter trailers the same distance and its worked great. I have experience towing utility trailers but I've never towed a car and I have some concerns.



First is which type of trailer to use. I'll be renting from Uhaul so I have the option of a tow dolly or an auto hauler. I'm aware of the limitations of backing up a tow dolly. What I'm most concerned with is the additional weight of the auto hauler vs the lack of brakes on the tow dolly. With the auto hauler I'm looking at a combined trailer/load weight of about 5000lbs with the added assistance of surge brakes on the trailer. With the dolly the combined weight is about 3600lbs without any trailer brakes. Is a 5000lb trailer with brakes safer than a 3600lb trailer without? Does anyone have some experience towing either of these trailers with their WJ?



Second, I do not have an additional transmission cooler but could install one myself for around $60. Based on my experience I don't think I'll need it if I use the tow dolly. Would I need this to tow the auto hauler or will the stock cooler be sufficient? Thanks in advance!