It's 81" from the floor to the bottom of the duct. Code in my area is 76" for the door -- this only gives me 5 inches for the door frame/header, which I think is not enough(maybe I'm wrong on this). I've thought about trying to move the ductwork up, but this does not seem feasible.
I'm in a condo, so I have to have an inspector see everything when I'm done. Maybe a pocket door is the way to go.