how would that help when you don't pull the clutch in when quick shifting?
bikes have dog gears and you only need the clutch when starting from a stand still. any bike can shift without the clutch. all the quick shifter does is cut timing to momentarily remove power to allow the shift lever to move the trans into the next gear without having to remove throttle to unload the trans, you can keep it pinned. completely unrelated to the clutch.
the quick shifter doesn't delay power application forever so you need to make a positive shift. do not leisurely click the next gear, if you want to do that then pull the clutch in. the dqs is meant for full throttle shifts that you bang into the next gear.
also, make sure you completely remove pressure from the shift lever after making a shift. if you maintain pressure until the next time to shift it may not engage fully into the next gear. so remove pressure completely, then preload the shifter with your foot slightly, when it is time to shift bang the next gear firmly then again remove all pressure and then redo it for the next shift.
point being, the issue you are having has nothing to do with the quick shifter mechanism. it is user error.