I think you would want a high CBD and almost no THC blend of oil. From what i have read and experienced our pets do not process THC the same way. Sadly, I thought it would be funny to blow smoke in my dogs face when I was a kid. He really liked the smell and taste and would chase the bowl around the room, but he got a little wigged out when he ran into the kitchen with a checkered tile floor
There are cannabis treats for pets that you can buy. I believe they are made from hemp oil. canna-pet is the brand. Are they effective? I don't know. Probably mostly hype.
If you get ambitious and make your own recipe for sale I own a few really good domains that are for sale regarding this topic.
If you are going to medicate the dog maybe make some olive oil or coconut oil at a really light dosage. For human consumption I use 1 tsp of ground bud for every tsp of oil... Maybe cut that recipe by 10x to try it out and increase strength over time.. Just a thought. I hope this helps and wish the best for your pet.
Maybe grow some of the high cbd strains.. I have grown two.