Scott Morrison, the prime minster, had the opportunity to purchase more vaccines, and was advised to "purchase as many as you can" by public health advisors. Instead, he did what he and the rest of the Liberal Party of Australia (conservative) have always done...
Not purchase enough, then shift the blame to the individual states and let them fight over what few vaccines were actually purchased.
There has been months of advertisements rolling, advising under 50s to head to their GP and get an Astrazeneca shot. I am in my late 20s, and have gone to my GP multiple times only to be told I'm not part of the roll out. The ads from the government tell me I can get a vaccine, but my GP says there are no vaccines.
Our government only know how to spin and market.
The Liberal party have literally been marketing a solution (get vaccinated) that they don't have, because they never had enough vaccines in the first place.
tl;dr Effectively most people (in NSW at least) haven't been able to get a Vaccine until very recently, and there's weeks of waiting to get a booking.
If you want a case study of a bad vaccine rollout. Australia is a good bet.
I think the larger but less spoken about issue is general apathy and a lack of urgency from the population. Our case numbers and deaths are incredibly low by most global standards. Melbourne has been in and out of lockdowns, but most of the rest of the country have been _mostly_ going on with business as usual. The biggest impact for people has been the uncertainty around interstate travel.