For outbound travel Australians are required to get a government exemption to leave the country. Australia also has far fewer inbound quarantine places per capita.
Also internally most states require entry/exit permits and frequently close thier borders to one another.
Australia screwed up the vaccination strategy. They bought AstraZeneca and relied on a domestic vaccine that was being developed which failed in trials.
Then the AZ side effects became an issue and there was no backup plan.
But even the AZ rollout was a debacle with no one sure if they were eligible or how to get it. And the Prime Minster excusing it all by saying "it's not a race".
If Australia had the vaccination rate of the US or the UK (which was absolutely achievable) then Australia would still be the envy of the world.
New Zealand also screwed up vaccinations by not buying AstraZeneca - as evidenced by the fact that they're several percentage points behind Australia and constrained by Pfizer supplies from overseas with no ability to rely on domestic or Australian manufacturing.
Australia ordered AZ from overseas, AZ manufactured locally, Pfizer, Novavax and now Moderna (as well as the UQ vaccine which as you mentioned failed).
Australia needed the doses in April/May, not September/October.
[1] https://www.abc.net.au/news/2021-07-09/australia-to-get-pfiz...
[2] https://www.health.gov.au/news/vaccine-operations-centre-wee...