How would Australia and the Dominions enter the war?

How would Australia and the other Dominions be drawn into the war?

They were part of the Empire but still had a choice; they are expected to join as they did historically, including South Africa.

The Dominions were part of the British Empire but were not mechanically compelled to declare war. Australia and the others had the option to abstain, yet they are expected to make the same decision they did historically. Even South Africa joined despite its internal political tensions. The answer separates imperial membership from the governments' actual choice to enter the conflict.