As the other member mentioned, your MDX can tow a max of 5000lbs.
The Auto Transport (2210lbs) and Altima (3447) yields a 5657lbs, which exceeds designed tow specs and is not advised. You break anything on the vehicle, your warrenty wont cover it and that transmission cooler is not going to help much either.
The dolly (750lbs) and Altima (3447llbs) yields a 4197lbs, which is much better for towing. However, the challenge is to equip the trailered vehicle with lights that hook up to the MDX and are DOT legal.
My Advise, rent a F150, rent an Auto Transport, load the altima and have a piece of mind. Make sure that the F150 has trailer harness, a lot of the rental places specifically do not have trailer harness.