The British were the only European power to seriously try to colonize Australia (and New Zealand). However, they were by no means the only country that had the opportunity or ability to do so; the Dutch (via the Dutch East Indies) and the Spanish (via the Philippines) already had a presence in the area, and the French or maybe even the Portuguese wouldn't have had too much trouble reaching and colonizing Australia (after all, the British did).
Bonus points if these colonies survive into the present day and result in multiple independent nations in Australia.