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I understand where you're coming from, considering the etymology of "kingdom", but given that it is still the United Kingdom of Great Britain and Northern Ireland, even under the rule of her Royal Highness, changing "kingdom" might be overkill. Also, "monarchy" refers to a system of government and not to the country or nation. If you really want to go that direction, it might be more appropriate to say "Dominion", but who wants to explore the Toy Dominion or Monarchy anyway? It would kill the storybook feel of the thing.