Whether you capitalize a dog's breed depends on the origin of the breed name.
Although the website for the American Kennel Club and dog-specific publications such as Bark magazine and Dogster seem to capitalize all the words in breed names, the Associated Press’s rule for dog (and cat) breeds is to capitalize the part of the name derived from a proper noun and lowercase the part of the name derived from a common noun.
Consider these names:
- English mastiff
- Yorkshire terrier
- Norwegian elkhound
- Bernese mountain dog
In those examples, according to AP style, “English,” “Yorkshire,” “Norwegian,” and “Bernese” are all capitalized because they are derived from proper nouns—the names of places.
On the other hand, "mastiff" is derived from the Latin "mansuétus" for "tame or mild," "terrier" is derived from the Old French "chien terrier" for "dog of the earth, land, or ground,” and “elkhound” is descriptive as is “mountain dog”—so those are all common nouns, which means those parts aren’t capitalized.
And for some breeds, all the words in the name are lowercase, such as “basset hound.” These hunting dogs were initially bred in France and Belgium, and “basset” means “low” in French, describing their lowness to the ground because of their short little legs. All the better to sniff for prey!
The Chicago Manual of Style doesn’t give instructions that are as specific as those from the Associated Press, but refers writers to Merriam-Webster dictionaries, which appear to generally follow the same guidelines as the AP.
Since styles seem to vary, if you’re writing about the Puppy Bowl, the best advice I can give you is to check the style guide for your publication, or if you’re writing for yourself, check a dictionary or choose a style you like and simply use it consistently.