you could have the Australian Republican Association becoming more popular in the late 19th century (due to pro-white autralia policies and anti- royal navy taxations) so that by the time of federation, Australia sees itself as all but a republic within the empire. When WW1 comes around, they feel that the conflict is of no concern to them and stay out.
WW2 though is a different thing. Fear of a japanese invasion meant that Australia would probably join the Allies no matter what. They might however wait until japan had expanded into the pacific before doing so.