Stuffy and dusty and you want to ventilate the room. First need to find out where all the dust come frome. If from outside, getting outside air to blow thru the house may solve stuffy problem but not dusty problem. If just pure ventilation regardless of dusty problem, you can place louvre above the door and window or even place ventilation fan at the window or ceiling.

In that case you can place louvre at both doors and windows. Modern room design is for aircondition, no airflow provided. Older house have louvre above every windows and sometime doors. Once you do this, you'll not able to solve dust problem since good airflow usually bring dust from outside. Air filter can't keep up with the dust unless you seal all ventilation holes. That is why I said you can't solve both at the same time with natural solution.

That's what I meant. It does not have to be above the door in your case but on the door itself if you do not mind. Another alternative is to open all the doors and windows for ventilation during the day and then close it up for the night with air filter and fan/air cond turned on. That is what many people did in order to solve the dust problem.