As SLumpp said, a good idea to get a complete brake inspection before initial towing if it’s been a while since service. Also a good time to really check out the system on the 08 trailer for any leaks or issues with that system as well. It kind of boils down to how much towing/driving will be expected out of the SUV.
Finally, with the information given on the Mitsubishi Outlander V6, towing cap is 3500 lbs-is there a “towing package” option that you have on the vehicle? Engine oil cooler, transmission cooler, etc? Does the SUV have the stock size tire/wheel package, as upsizing may effect performance?
Just a few more observations from the sidelines. If I had a “do over” I would have gotten a little bigger SUV for my wife so we could tow the camper with my truck and our other toys with her SUV…motorcycle/trailer, bicycles, kayaks/canoe trailer.