Kyouko's not a dog

Neither said:
Kyouko's not a dog

Don't think too hard about it, it's adorable and thats what matters

Momiji's not a dog too.

Yeuyo said:
Momiji's not a dog too.

But she's part of the canine family

Neither said:
Kyouko's not a dog

But she does make a very cute one.

Neither said:
But she's part of the canine family

As yamabikos are mythological beings, you have some liberty on choosing their families. The monster looks to me like an overgrown pekinese, anyway.