Ok, this took me some time to think about. Syndicalism isn't my specialty. If Marxism didn't get any traction, Syndicalism might be attractive to those on the bottom of the economic totem pole. Prior to fascists takeovers in Spain, in OTL, there were businesses where 3/4 of the shares were expropriated by the government and given to a kind of fund that paid to the workers proportional to their gross pay. The plan was to later ban the import of all goods from companies that didn't follow this scheme or tax away 75% of the profits from foreign companies' Spanish operations that put their products in Spain, and give them to the Spanish workers.
Now the fact is that in OTL France, the communists got something like 4th place in elections before WW2. That doesn't sound too impressive until you remember there were dozens of parties that got parliamentary seats. If Soviet Union implodes early and has massive famines when Lenin dies, then people might conclude communism is nothing more than a dud ideology and Lenin was simply a dictator that kept hope alive and Soviet Union running. With communism discredited, Syndicalism might end up getting traction in France, but they might attract run of the mill left wingers too instead of just the radicals. So you might have france running the transition from Socialist to Syndicalist in say 1936.
Now if Germany somehow wins WW2 (uhhh... I don't know. If they were "vanilla" fascists instead of genocidal evildoers and stuck with the Munich agreement, there is actually a plausible British backed Germany vs Soviet Union and Poland Scenario, but Hitler kind of nixes that line of events) with Britain not getting involved (say... the Syndicalism or something discredits France in British eyes and the Germans keep the Munich agreement and don't go mucking around with neutral countries like Denmark but simply focuses on the ideological enemy in Soviet Union and the hated French for imposing Versailles), there would be Syndicalists who can't go back home. They'll fall into various places and try to spread their ideology.
In Australia, they might bump into the labor activists and find some sort of compatibility. Now here is the problem. To have the workers get the lion's share of the profits, the company shares need to be expropriated, or someone needs to compensate the previous owners.
Pretty much any country in the Anglo-sphere values property rights and Australia is descently loyal to the crown. Expropriation doesn't sound very nice. Compensating sounds expensive. At best, maybe Australia runs a budget surplus for several years, perhaps cutting defense and social programs, and fixes their currency to the pound to save up to transition to Syndicalism?
Ok, it's a long shot, and the POD would be Lenin's death, so...
If we have a successful Syndicalism in Europe, maybe Australia might slowly adopt it, but OTL France was kind of a mess in the 1930s, so having an early allied win to WW2 with a Syndicalist France doesn't scream "workers paradise, copy me" since the economy had some issues and the social fabric was actually unraveling within France, so no mater what their ideology might be they wouldn't look great.