No. Not false.
While Australia did federate in 1901 and the Australian Constitution came into effect on that date, the British Parliament retained the right to pass laws concerning. Australia under the Colonial Laws Validity Act of 1865. This Statute of Westminster of 1931 amended that situation by stating that the British government could no longer make laws for the Dominions (at that time, Australia, New Zealand, Canada, Newfoundland, South Africa, and the Irish Free State) but also contained provision that the Statute of Westminster would not take effect in Australia until the Australian government ratified it. The Australian government finally ratified the Statute of Westminster on the 9th October 1942.
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