Toadinthehole: Round these parts (NZ) the Commonwealth has become invisible
You are to be envied! So, you no longer have things like official royal visits solely to drum up warm fuzzy feelings for the Commonwealth, the Union Flag has been removed from your own, the image of the Queen no longer appears on new coins or any stamps, you didn't participate in the recent Commonwealth Games, "God Save the Queen" is no longer one of your two official national anthems - and, most important of all, you no longer have a Governor-General who is trotted out for some official occasions.
Oh, the Monarchy cost New Zealand $4.5 million pa (2010): only $1/per person, but money that would hire, for example, approximately 450 nurses.
There was a kind of commonwealth of dominions before the war (Canada, Newfoundland, South Africa, Australia, NZ, UK), not part of the Empire, and all independent of one another, just under the same monarch.
The countries which you mentioned, plus the Irish Free State, were "autonomous Communities within the British Empire" and were British Dominions which were definitely part of the "His Majesty's dominions" (note the lower case to represent the difference). His Majesty's dominions referred to the British Empire as a whole. Whist semi-independent, these Dominions were definitely part of the Empire.