No. An early name for Australia was New Holland. It is thought that the name New Zealand may have been a reference to this as both Holland and Zealand (Zeeland) are parts of what is now called the Netherlands.
James Cook only travelled to New Zealand and Australia once.
Tasmania
The country off the southeast coast of Australia is New Zealand.
The New Zealand Warriors is the name of the New Zealand Rugby League team that plays in Australia's NRL competition.
Australia and New Zealand are separated by the Tasman Sea
Yes, New Zealand is a country situated southeast of Australia.
New Zealand & Australia
The Tasman Sea is the name of the stretch of ocean between Australia and New Zealand.
Australia, New Zealand, Canada and Ireland were all once part of the British Empire, as they were British colonies. Australia, New Zealand and Canada are now all members of the Commonwealth of Nations. Ireland is not a member of the Commonwealth of nations.
The only country in Australia is Australia. There are no other countries in Australia.
The name given collectively to Australia, New Zealand and surrounding islands is Oceania. It is not considered a continent but instead is a region or the world.
Australia never changed its name to Oceania. Oceania refers to Australia, New Zealand and surroundings.