Using "he" or "she" for an animal not a person?

Yes, animals of a given gender can be referred to using he or she as appropriate. For example we might say

The female dog runs across the field. She is fast.

However, when referring to an animal of unknown gender, it is acceptable.

The dog runs across the field. It is fast.

This is in contrast to people. If a person is of unspecified gender, one is more likely to use he or she. In fact, the correct gender-neutral third-person singular pronoun to use for a person is rather controversial, as shown in this discussion.

Regardless, for animals the answer is fairly clear-cut: use he for male animals, she for female animals, and it for animals of unspecified gender.

Personal pronouns (He) can only be applied to male human or domestic animals. Personal pronouns (She) can only be applied to female human or domestic animals.