OILS TO AVOID WITH DOGS?
Oils to avoid topically and internally with dogs: Birch, Melaleuca (Tea Tree), and Wintergreen. Use caution with hot oils such as Oregano, Cassia, Cinnamon, Clove, Rosemary, and Thyme.
DIFFUSING AROUND PETS?
ANSWER FROM Dr. Janet Roark:
Diffusing around pets: If you have a very small room where the animals like to hang out with you, diffusing 2-3 drops in a water diffuser of nearly any oil is probably fine. However, every animal is different and some have different tolerances. If their behavior is normal within the first 20 minutes of diffusing a new oil, then it is one your animal is probably not sensitive to.
Using large amounts of oil in your diffuser, not adding enough water, or diffusing oils they are sensitive to is never a good idea.
I diffuse everything in my own home and have for years without any problems. So on the website at www.essentialoilvet.com/safety it does address which oils to be careful with around dogs and cats, and you are correct, this does apply to topical and internal use.
I always recommend observing your pets behavior within the first 20 minutes of diffusing a new oil to ensure all is well.