We owned a Coleman tent trailer with about your same specifications. Originally towed it with a Toyota T100 which wasn't ideal. The drive train was fine but the short wheelbase and long rear overhang made for a choppy ride. Later moved on to a Nissan Titan which pulled the trailer well unless the water tank was full then it swayed viciously. Reese makes the steadi-flex lightweight weight distribution hitch with anti sway which will improve your tow regardless of vehicle.
I also believe you will be happier with a full sized crew cab truck as your family grows. Many great times and memories with that tent trailer.