There is nothing even vaguely resembling of a canine in the game; however, in the downright impossible situation where a dog in real life was controlling Mario and was consequently horrible at the game, it is possible that said character vaguely representing the player (in this case a dog) could perish. As long as you aren't a dog yourself, there is no need to worry about seeing such a catastrophic and tragic outcome.
Any rumors that Mario is 35 and Princess Peach is 19 is an urban legend based off of a misunderstanding as the Google results showed the ages for their self-titled games and not the characters