Burn the windmill (by windmill I mean the rotating "fan") on the outside using your torch. You can access the windmill from behind the central bonfire. I killed the boss without doing this but I went back to try and can confirm it works. The way I did it was from the lower floor where you can access the windmill, you can climb a little bit and if you have the torch you will be able to set fire to the "fan". You can confirm it worked because the gears inside will stop turning and most of the poison will be gone (e.g. The one before the entrance to the boss). Note that doing this does not COMPLETELY remove poison from the queen's chamber, you will still get poisoned on entrance, but the inner circle will be poison free so you can heal and she can't.
Btw if you could return the favor I have a small problem with this: http://www.gamefaqs.com/boards/693331-dark-souls-ii/68745461