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from Latin Terra Australis (16c.), from australis "southern" + -ia. A hypothetical southern continent, known as terra australis incognita, had been proposed since 2c. Dutch explorers called the newfound continent New Holland; the current name was suggested 1814 by Matthew Flinders as an improvement over Terra Australis "as being more agreeable to the ear, and an assimilation to the name of the other great portions of the earth" ["Voyage to Terra Australis"]. In 1817 Gov. Lachlan Macquarie, having read Flinders' suggestion, began using it in official correspondence. The ultimate source is Latin auster "south wind," hence, "the south country."
The Latin sense shift in australis, if it is indeed the same word other Indo-European languages use for east (see aurora), for which Latin uses oriens (see orient), perhaps is based on a false assumption about the orientation of the Italian peninsula, "with shift through 'southeast' explained by the diagonal position of the axis of Italy" [Buck]; cf. Walde, Alois, "Lateinisches etymologisches Wörterbuch," 3rd. ed., vol. 1, p.87; Ernout, Alfred, and Meillet, Alfred, "Dictionnaire étymologique de la langue latine," 2nd. ed., p.94. Or perhaps the connection is more ancient, and from PIE root *aus- "to shine," source of aurora, which also produces words for "burning," with reference to the "hot" south wind that blows into Italy. Thus auster "(hot) south wind," metaphorically extended to "south."
Note: The first settlements there were penal colonies for British convicts.
Note: Its aboriginal tribes, which still exist today (see aborigines), are thought to have migrated from Southeast Asia twenty thousand years ago.