Biographies of animals are not a very common genre, although it is not difficult to find examples with a bit of digging:
- Flush: A Biography (1933) by Virginia Woolf is the "imaginative biography" (Wikipedia's description) of a dog. Its entry in the Library of Congress) simply classifies is as "biographical fiction".
- Bobbie, a Great Collie by Charles Alexander (1926) is about Bobbie the Wonder Dog. The Library of Congress does not identify the book's genre.
- Comanche: Story of America's Most Heroic Horse (1951) by David Appel is about of one of General Custer's horses. Its entry in the Library of Congress does not mention a genre.
- Reckless, Pride of the Marines (1955) by Andrew Geer is about a war horse that served in the Korean War. Neither the Library of Congress nor Amazon.com provide genre information for this book.
- Soldier Bear (1970) by Geoffrey Morgan and Wiesław A. Lasocki is about a bear named Wojtek that was enlisted in the Polish II Corps. The Library of Congress does not specify the book's genre but considers it as "juvenile literature" (see "LC subjects").
- The Judy Story: The Dog with Six Lives (1973) by Edwin Varley is a book about a ship's dog in the British Royal Navy. The Library of Congress does not know it; Amazon.com only has it second-hand and does not classify it as any specific genre. Judy: A Dog in a Million (2014) by Damien Lewis is a more recent book about the same dog. Neither the Library of Congress nor Amazon.com provide genre information for this book.
- Dewey: The Small-Town Library Cat Who Touched the World (2008) by Vicky Myron is the "biography" of Dewey Readmore Books, the library cat of the Spencer Public Library in Spencer, Iowa. The Library of Congress does not classify this book as biography (but it has "Library cats--Iowa--Spencer--Biography" listed as a subject). Amazon.com lists it under "Books > Biographies & Memoirs > Regional U.S. > Midwest". Wikipedia's editors have not bothered tagging the article about the book with anything referring to "biography".
- Hachiko : the true story of a loyal dog (2004) by Pamela S. Turner in the Library of Congress does not have a genre identification, but the term "biography" is used in the "LS Subjects" ("Dogs--Japan--Tokyo--Biography.").
A biography of an animal can be called in "animal biography". However, books about animals are sometimes classified as "juvenile literature", sometimes as "biography", depending on the audience rather than the individual whose live is being described. I have never come across the term "animal biography" in a dictionary of literary terms and don't expect it to become a literary term in the near future.