There's a whole lot more than three, and you didn't specify whether you meant Commonwealth Dominions (who acknowledge the British monarch as their own Head of State), or Commonwealth of Nations members (to whom the British monarch holds no status, but with which trade an other agreements exist with the British). Three Commonwealth Dominions include Canada, Australia, and Barbados. Three Commonwealth of Nations members who are not Dominions include South Africa (for better or worse), India, and Singapore.
Dominions
Dominions
Archaea, Bacteria, and Eukaryotes
King Edward VII, King of the United Kingdom and the British Dominions, Emporer of India.
The British Empire comprised the dominions, colonies, protectorates
Canada, Australia, and New Zealand.
Nationalists, Unionists and the British Government.
It was one of the Dominions of the British Empire, and therefore committed to defending the interests of the UK.
Neither New Zealand or Australia are "dominions of England". Both are independent countries, with a parliamentary democracy. There is The Commonwealth, which is composed of many of the former members of the British Colonies, but not all Commonwealth members are ex British colonies, nor are all ex-colonies members of The Commonwealth.
They do have a connection to the British Empire - so much so, that they're even one of the 16 Commonwealth Dominions which acknowledge the British Monarch as their Head of State.
"His Majesty George V, by the Grace of God, of the United Kingdom of Great Britain and Ireland and of the British Dominions beyond the Seas, King, Defender of the Faith, Emperor of India", until 1927, when it was changed to "His Majesty George V, by the Grace of God, of Great Britain, Ireland and the British Dominions beyond the Seas, King, Defender of the Faith, Emperor of India"