Not sure why you got downvotes but 100 percent Australia's slow ass Vax rollout is the result of a "conservative" government. Though they are closer to resembling an authoritarian corprotocracy rather than anything truly conservative or liberal.
So yes, probably because of this conservative government. Even because of these conservative governments (State and Federal).
But not simply because of a conservative government.
Being a conservative government has nothing to do with the slow Vax rollout. Over-reliance on AstraZeneca is to blame with no plan B.
NZ planned to use Australia’s AstraZeneca vaccines too, and has since dumped that plan altogether, has been scrapping together whatever Pfizer it can get and recently found a supply of the US’s unwanted J&J vaccines.
The fact is the Australian federation model has an odd separation of responsibilities which makes this challenge uniquely difficult for Australia.
The state governments haven't failed on health though? The federal government explicitly declined to let the states run the vaccination program in the way that they wanted and instead went GP-first (GPs being beholden effectively to the feds).
This is a nothing statement. The state based health services have generally been very well run, with the exception of contact tracing in Victoria during 2020.
The federal health responsibilities (vaccines, quarantine and PPE provisioning) have all been spectacular failures.