Do not routinely capitalize the names of dog breeds. Many breed names are composed of proper nouns that you capitalize and generic terms (like retriever or terrier) that you lowercase. 

Breed names are often composed of a place-name, as in these references to the breed’s country of origin:

French bulldog

German shepherd

Irish setter

Portuguese water dog

Sometimes the place-name refers to a region within a country:

Airedale terrier

Akita

Brittany spaniel

Labrador retriever

A generic term of foreign origin might also be combined with a place-name:

Lhasa apso

Another formulation for breed names includes the name of the person who created the breed:

Doberman pinscher

Gordon setter

Jack Russell terrier

Many breed names are composed entirely of generic terms, even though the terms may no longer be common parlance or may be of foreign origin:

affenpinscher

cocker spaniel

miniature schnauzer

Yet other breed names are capitalized according to convention and for clarity:

Old English sheepdog 

Shiba Inu

These same guidelines apply to other animal breeds, like cats or cattle:

Maine coon

Texas longhorn

Consult a dictionary like Merriam-Webster when you’re uncertain.