My dear one,
Regarding purification for yourself and your dog, take strong refuge in the Buddha and think that the Buddha sends light to yourself and your dog, and to any other animals or beings you want to think about. Think nectar comes from the Buddha and purifies the negative karma, created from beginningless time, of yourself and the dog and other beings you are thinking about.
Then recite the refuge prayer. Keep reciting the refuge prayer while visualizing the Buddha sending nectar out of his compassion and loving kindness, like sunlight, to yourself and your dog. It’s like switching the light on in a dark room; it totally purifies the negative karma created since beginningless rebirths. You can keep the dog nearby when you do this so the dog can hear you reciting the refuge prayer. This leaves an imprint on the dog’s mind and plants the seed of enlightenment.
If there is no stupa near where you live, then maybe you can go to a center that has a stupa. If you are able to go there that would be very good, then you take your dog around the holy objects, the stupas. Go around the holy objects as many times as possible with the dog. This purifies the negative karma collected since beginningless rebirths, therefore go around as many holy objects as possible with the dog.
If you go to a center maybe you could stay for one week or a weekend and bring your dog, and then you can go around the holy objects every day. You could do sessions four times a day, reciting refuge, then nectar comes from the holy objects and purifies yourself and the dog.
This is my advice at this time. Later if you want to ask for more practices you can send me an email, but first do this to the best of your ability.
Any practice that you do, you can recite it out loud so your dog can hear. This also helps to purify.
With much love and prayers ...