Cats can certainly be allergic to essential oils most cats will be immune by the time that they're 6 months old. If you find that your dog doesn't respond to catnip then you'll need to administer a diluted form of the essential oil. It's also possible for some dogs to have an adverse reaction, particularly if they have sensitive skin or suffer from a condition such as atopy (dog allergies). If you're using it for a soothing effect then make sure that you don't overdo it and ensure that your dog is always supervised when they're near or handling the essential oil.