Wikipedia is a wonderful resource.
Australian English began to diverge from British English after the First Settlers, who set up the Colony of New South Wales, arrived in 1788. By 1820, their speech was recognised as being different from British English. Australian English arose from the intermingling of early settlers, who were from a great variety of mutually intelligible dialectal regions of the British Isles, and quickly developed into a distinct variety of English which differs considerably from other varieties of English in vocabulary, accent, pronunciation, register, grammar and spelling.
The most distinctive influences on New Zealand English have come from Australian English, English in southern England, Irish English, Scottish English, the prestige Received Pronunciation (RP), and Māori. New Zealand English is most similar to Australian English in pronunciation, with some key differences.