Every pet is different, but it is good to be careful. Using a diffuser can be safe and calming for some dogs. Try using a diffuser that is adjustable so you can reduce the amount of essential oil because remember, dogs have an extremely sensitive sense of smell!
There are some oils that are not recommended for use around dogs, so check with your veterinarian first. Clove, Anise Juiper, Wintergreen, have been shown to cause negative reactions like allergies or skin sensitivities. However, Chamomile, Lavender, Peppermint, Ginger are all safe to use in small amounts.