When burying a pet you should dig down as deep as 3 feet as a minimum.
For a larger pet such as a large dog you might want to dig down as far as 4 feet if you can to prevent other animals from smelling the scent of the dead pet and digging them up.
But if you can only dig down 3 feet that is usually deep enough to bury any pet including a dog or cat.
You can either put the pet in a coffin or container and bury the pet that way or you can just place the pet directly into the ground and cover them up with dirt.
There's no need to have a pet cemetery as you can just dig a hole in your backyard and bury the pet there.
Just make sure there are no utilities in the ground where you are digging and you can call 811 and they'll send people out free to mark buried utilities.
If you know nothing is there then you can just dig and bury the pet.