Malcolm Turnbull
Not only does the Prime Minister of Australia have pet dogs, he also maintains a blog about dogs. Although he may not be very active on the blog (obviously) what he maintains is believed to be an account of his own dogs Roxy, JoJo and Dusty.
Narendra Modi
The Indian Prime Minister is famous nowadays for the dog remark that he passed in the Parliament and politicians are taking him with a head on approach indignantly. He owns a Golden Retriever and various sources confirm that he is very affectionate towards the dog, letting him taste his food occasionally right off the plate.
