I must tell you that pet aromatherapy is not my area of expertise. I did want to bring up the subject, if for no other reason than to keep someone from accidentally poisoning a beloved family pet.
Essential oils can be used for dogs in a variety of ways, from bathing to calming the nerves, to flea and tick prevention. Always dilute essential oils for use on a dog at 20% the amount used on a human. (If your own blend calls for five drops of lavender, then the dog only gets one drop).
Never use essential oils on cats, ferrets, birds, or fish.
Felines have no means of processing essential oils; their livers cannot filter them out so the oils build up and become toxic. It is my understanding that the same applies to pets such as ferrets. Keep heavy usage of diffused essential oils to a minimum.
For birds and fish, even breathing in a consistent supply of essential oils can be deadly (fish, by way of the fumes settling on the water). Do not use your aromatherapy diffuser in the same room as your birds or your fish tank.
If you have a pet other than mentioned above, it does not mean that they can safely use essential oils. There are numerous and more detailed resources about pets and essential oils. If in doubt, consult your veterinarian.