From the Online Etymology Dictionary:
Italy
from Latin Italia, from Greek Italia, perhaps from an alteration of Oscan Viteliu “Italy,” but originally only the southwestern point of the peninsula, traditionally from Vitali, name of a tribe that settled in Calabria, whose name is perhaps somehow connected with Latin vitulus “calf,” or perhaps the country name is directly from vitulus as “land of cattle,” or it might be from an Illyrian word, or an ancient or legendary ruler Italus.
Australia
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.”
In short, “Italy” grew out of other uses, while “Australia” was consciously applied. I suspect that there is a lot to be said about the -y and -ia suffixes, but I don’t actually know what I’m looking for, so I can’t help you there.