Examples of proper nouns:
* People: John, Mary, Queen Elizabeth
* Places: London, Mount Everest, The Great Wall of China
* Things: The Eiffel Tower, The Titanic, The Mona Lisa
"Dog" is a common noun, referring to the species in general.
If you want to refer to a specific dog, you would use its name, which is a proper noun:
* "My dog's name is Max." (Max is the proper noun)