We actually have quite a large Irish ancestry population, even those who still self-identify, but the relative Scottishness of British settlement in Canada versus the relative Irishness of Australia was actually a quite long-in-use way of describing Canadian history to ourselves. I think I have encountered Australians who do the same comparison, so the idea had legs for many generations.

There are a number of documented cases of transportees sent to America who simply bought a ticket and sailed right back to England. Australia was a bit harder to return from…

However, 32 years later, in 1820, Australia’s European population still consisted of 84% of convicts and former convicts, and convict transport from Britain to Australia did not cease until 1868

Tendentious.
Australian population in 1868 was 1.5 million, and total convicts transported topped out at 167 thousand. The reason it could be 80% convict in 1820 was because the population was 34 thousand.
Of note, the usual proportion of criminal families in European populations is ~10%.