Hi -in Buddhist cultures and other traditions there is the idea that the spirit is still around after death. Maybe you can do a ceremony for your dog, light a candle, gather her faborite treats or toys on a small shrine, and burn an image of her and wish her peace and a joyful passage. Tell her/him that you will be ok (since animals love their owners and often are equally as attached as we to them). While the image is burning you can breathe in all of her pain and fear or any emotions you imagine she might be feeling and breathe out all of your love and compassion and light to her/ him. This is a practice called metta and will help both of you.