I have towed my Mini with my 2010 MDX for the last 4 years. I have a 16' flatbed trailer and the MDX pulls it just fine. Just watch your weight carefully. Gross combined weight rating is only 10100lbs. With the Mini and tires on the trailer, and 2 adults and gear in the car I crossed the scales at 9980lbs with a full tank of fuel. Most 16' open trailers weigh about 1500lbs, and you want to stay 5-10% under your max tow rating for a safety margin. Don't even think about an enclosed trailer. Even if you could find a light enough trailer, the MDX is not long enough or heavy enough to deal with the sway as the wind beats around an enclosed trailer.

A couple of upgrades I have made over the last few years that are not necessary, but help:

Trailer brakes. The first year I was using a borrowed trailer without brakes. It worked, but trailer brakes make a huge difference in control and safety. The factory MDX tow package comes with a 7 pin connector, and there is already a harness for the brake controller under the dash. I highly recommend a trailer with brakes and a good brake controller (I use a Tekonsha p3)

Race Ramps. The angle on the rams are most likely going to be too steep. Race Ramps are pricey, but well worth it. 

Helper air bags. A fully loaded trailer will cause the rear end of the MDX to squat quite a bit. I have added a set of air bags inside the rear springs which helps keep the rear end from squatting so much. It is a more comfortable ride, and handling is better as it puts the nose of the car back down. (I have Air Lift 1000 bags. Cheap and easy to install)