With the Integra you will be getting close to the 5,000 pound limit of the 4Runner. I am guessing about 4,000 pounds with the car & trailer. I would get a wieght distrubtion hitch and really good brakes on the trailer. With 130,000 miles on the trailer you will be testing the rig. You might consider a transmission cooler and at the very least get your automatic transmission oil changed.
Still, with the way our 4Runners are built I would suspect it will do O.K. Be sure to put on the "ECT" button and leave it in third gear. I have a trailer and it wieghts on 2,200 pounds. It does fine. Sometimes I forget it is there. I doubt you will forget with 4,000 pounds behind you.