Check the payload. Loaded up luxury SUVs tend have the same GVWR as the base models which can weight 500 pounds less. So, the Infinity QX would be the same as the base Aamada. 2006+ vehicles have a Tire and Loading sticker like this one which give as equipped payload, with a full tank of fuel. I have not personally seen any Armadas or QX, but I have seem highly optioned competitors under 1200 pounds.
Payload should be enough for the family, things to occupy their time while traveling, and trailer tongue weight.