Well made and interesting, and sure to be a great addition to character options in some darker campaign settings. It also seems well balanced against the other backgrounds in the skill proficiencies and starting equipment.
The plague doctor background does what backgrounds should; give players a solid starting point in character creation, and helps anchor them in the world. The various tables all contain strong options to generate, through choice or rolling, a character with a well defined personality.
The plague doctor is overall a great background, and suitable for classes such as ranger, rogue, and wizard. Of course, any class can come from any background, and "mismatched" classes and backgrounds can create unique interesting characters. However, A cleric or paladin from the plague doctor background would be counter to it's whole point, but I would be surprised if a player would be unable to make even THAT disparity work.