Oho! If the ban failed, that suggests that on the whole Australians didn't think it was very realistic for Communist Australians to take over.
If the ban is imposed, that's a sign that a lot of Australians think there is something to worry about. And the very act of declaring the Communists outlaws might well have a boomerang effect, making them seem more legitimate and serious.
Particularly if things seem to be going wrong under leadership purged of all taint of Communism.
So yes, a POD earlier than 1951, to explain why the ban does happen then, but it could be a subtle one.
I suppose that OTL Australia had pretty good times in the 1950s and '60s. What if this were not the case?
I see. I did a presentation on the Constitutional Limitations of Australian Government on this very matter. Timeline of the matter is:
13 March 1950
Communist Party Dissolution Bill [No. 1]
Result: Blocked
*27 April 1950
Communist Party Dissolution Bill [No. 2]
Result: Passed
14 November 1950*
Australian Communist Party v The Commonwealth*
Result: Bill is Rejected
22 September 1951
Australian Referendum, 1951
Result: 50.56% Oppose the Question
Opnion of other Australian factions in this time period:
Labor Party: “Fascist and wrong...”
Democratic Rights Party: “Constitutionally incorrect”
Young Liberals: “An abuse of... Australian law”
Wasn't a referendum over the CPA really, more over the limitations that the Menzies government had. Also seriously wrecked the ALP and that's why Menzies lasted so long.