Aww, the baby is playing mommy. Many a poor kitty and puppy has suffered the loving touch of a well-meaning little girl. I probably did something similar in a moment of lax supervision. I do remember putting our cat in my doll stroller. She was cool with it when it suited her.
No, your stove will be as black as this cat after polishing. Black being the desired color, as it doesn't show the soot.