In most general texts, use lower case for animal breed names, except for proper nouns:
Labrador retriever [dog] golden retriever [dog] exotic shorthair [cat] Burmese [cat]
However, formal breed names often have initial capitals in publications in a specific field (eg dog or breeding associations, kennel clubs), but not for generic groups:
Exotic Shorthair American Shorthair but shorthairs
Cavalier King Charles Spaniel Springer Spaniel but spaniels
Check with your authors and publishers, and maintain consistency.
See Livestock for further information on livestock breed names.