New Zealand's national carrier is Air New Zealand and is the main way of traveling by air through New Zealand. New Zealand's next major carrier is Qantas, the Australian national carrier.
There are other main players in the competitive trans-Tasman market (the market between New Zealand and Australia that crosses the Tasman Sea) they include Jetstar, Virgin Pacific, Freedom and Emirates.
Virgin, Jetstar and Freedom are the budget airlines. Jetstar is a company that is owned mainly by Qantas and Freedom is mainly owned by Air New Zealand. These three airlines are the airlines you would concentrate your search for cheap New Zealand to Australia airfares, but sometimes the major players offer better deals so do not think that because they are budget they are the cheapest. These airlines keep the prices competitive so you as the traveller will get some great deals if you "shop around".
New Zealand also has many small airlines to enable you to see some of the wonders of New Zealand including Origin Pacific and other scenic flight airlines from the smaller towns and cities.
Safety standards in airports and on airlines that travel the New Zealand skies are among the highest in the world, with strict air safety regulations. When you arrive in New Zealand there are strict rules and instant fines for bringing undeclared food items or anything that could effect the delicate New Zealand environment and bio-security of the country.
Most airlines leaving from New Zealand airports are also not as strict with the check in times as other countries with higher international safety concerns.
Have fun flying the New Zealand skies. You will enjoy the friendship of New Zealand airline staff and the service that you will receive.