Britain invades Hungary sometime in the late 1700s/early 1800s and ships the Royal Family off to one of the penal colonies in Australia. Hungarian refugees flee to join their King, form a colony they call New Hungary. The Rum Rebellion or some ATL equivalent goes sour, some Australian colonies declare independence and form a union with New Hungary, which drops the "New" after Britain turns their old country into a bunch of... crumpet farms? Statues of Horatio Nelson? I dunno. Anyway, badda bing badda boom, Australia-Hungary!