"Dare" means "who". It can't be used for animal.
Kono/sono/ano/dono is attributive. It's used when modifying nouns. On the other hand, Kore/sore/are/dore performs as a noun.
e.g.
This is an animal.
Kore wa dōbutsu desu.
That animal is dog.
Ano dōbutsu wa inu desu.
Thus, kono dōbutsu means "this animal"