Does Jabberwocky count as an animal poem?

Jabberwocky is certainly described as a nonsense poem.

Jabberwocky does use "nonsense" Words made up by the author, but it tells a specific (and interesting) story, and you gain the knowledge of what the Words mean, at least approximately, from the context of the poem. It's part of the process of a living language. Once someone uses a Word to mean something, other people pick it up, and it gains meaning to a general group. Many of the Words in Carroll's poem have been used by other authors and now are part of the language, even though they started out as Words that only made sense to Lewis Carroll.