There is a forum for pet health here. You would get better results posting your question about your dog's yeast infection in that forum.
I know this much.....if you apply oil of oregano topically you need to dilute it with olive oil or another oil. It will burn the skin if not diluted. I do not know how much to dilute it. Hopefully some one else knows and will tell you.
Lots of "oil of oregano" is not even oregano, it is thyme. The one that is best is by North American Herb and Spice. It sounds expensive, but is very concentrated. It has P73 on the label. It is authentic, wild oregano. Check out the link below.
I have used "oil of oregano" by NOW foods....and would not purchase it again. I have also used "oil of oregano" by Wellness and it is even worse thatn the one made by NOW foods.