Ringworm?
Those spots look like possibly ringworm which is a fungus. Any more similar spots elsewhere? Stuff is highly contagious, to humans too. If you can touch the doe, apply some fungus ointment (the athlete foot cream for humans OTC is fine), or get anti fungal liquid/treatment from TSC or Jeffers Livestock web/catalog. Takes diligence to get rid of it. Definitely continue treatment after spots disappear or it might be right back. Wear gloves and wash hands or any other part of yourself that might have touched the spots.
