You have to steer it back with "No I'm a dog"
Doesn't work. ChatGPT realizes you're roleplaying and still treats you like a human. It even generates two alternative paragraphs of advice, one labeled "if we're staying in character" and one labeled "if this actually happened to a real dog". The latter is of noticably higher quality, too.
I suppose that, on the Internet, ChatGPT really does know that you're not a dog.