Yes, I am aware that what we know as a plague doctor's outfit (thick waxed leather coat, mask, wide-brimmed hat, etc) was not invented until the 1700's. However, plague doctors did exist earlier, though little is known about their costume. Some sources claim that the beak mask itself predates the rest of the costume, originating sometime during the Middle Ages.

This makes sense, given that its purpose was based on the miasma theory of disease (the idea that diseases are spread through foul air), which was in favor during both the Renaissance and the Middle Ages. It stands to reason that someone would have developed some sort of respirator.

Moreover, a quick Google search for "medieval doctor" will show you that the beak mask is deeply-rooted in people's imagination of not only the plague, but also of the Middle Ages in general.

So, based on all that, I made a skin. It's plausible that the mask existed during the Plague outbreaks of the Middle Ages, and I've used my imagination to design medieval-looking clothes for the rest of the body, as opposed to using the specific uniform that I know was invented during the Renaissance. Chalk it up to artistic license.