Exchange online services
In almost any country, a person who wants to buy bitcoins can use the exchange service. The largest aggregators of such services are localbitcoins.com and www.bestchange.com. You need to decide how to buy cryptocurrency (using a bank card, money transfer, electronic payment systems, etc.) and choose a right trader. Pay attention to the reviews. It is worth choosing a seller without complaints and lots of good reviews.
Direct buying: There are a number of opportunities in Australia. Bit Trade supports the POLi-Payments payment system, Cointree supports both options, bitcoin.com.au allows you to buy bitcoins by for paying them at kiosks, Coinjar not only sells bitcoins, but also supports its own Bitcoin wallet.
Exchanges: There a stock exchange called Independent Reserve is working in Australia.
Direct buying: You can buy Bitcoins on the Coined.co.nz platform via online banking transfer. Vimba offers a wallet and the opportunity to invest in Bitcoins regularly using automatic bank transfers.
Exchanges: NZBCX is a fully featured bitcoin exchange-trading platform.