Australia has got lucky and you should be grateful. It will largely avoid the severe and deadly over-reaction that the rest of the world has engaged in.

Firstly, given this is a coronavirus the chances of 'eliminating' it are zero unless you plan for Australia to cut itself off from the world harder than North Korea. It's infectious, it spreads. People travel. The virus will come back when your winter arrives.

But why do you even want "zeros for daily infection"? You don't chase that for the flu, and the evidence gets clearer every day that in fact, despite all the protests to the contrary, COVID-19 is no more dangerous than a bad (but regular) flu season. This wasn't apparent at first but we know a lot more than back in February. For instance it's now known not to over-use ventilators, as they can make the situation worse rather than better. In addition it's known that despite initial panic, nowhere has actually run out of ventilators, not even in Italy!

This site is an excellent collection of links with many doctors and professors stating the "similar to flu" opinion, along with links to raw data so you can check yourself:

https://swprs.org/a-swiss-doctor-on-covid-19/

But you can also just look at the mortality data for Europe:

https://www.euromomo.eu/

All-cause mortality peaked at about 85,000 per week (subject to adjustment), vs the flu season of 2017 where it peaked at 70,000 a week. So COVID-19 has been, so far, about 20% worse than the flu was that year.

I guess some believe that lockdowns could push infection rates to zero. But there's no reason to believe they make much difference. Sweden's course of infection is no worse than average for Europe, and they didn't close restaurants or hairdressers or building sites. If lockdowns had the hypothesised impact Sweden should be by far leading in mortality by now but they're not, moreover most of their deaths seem concentrated in nursing homes for which lockdowns don't do much. This is also seen in Belgium (50% of all deaths in elderly care homes) and has been seen in Italy, where some nursing homes became nearly abandoned after the care workers (many foreign from eastern Europe) fled at the start of the lockdown.

Sweden is also seeing a higher impact in their migrant population for reasons currently unknown, but in the USA African-Americans are doing worse than average, so it may be skin colour related for biological reasons.

Some people are trying to distract from this by comparing Sweden to e.g. Denmark, but unlike what you suggest here lockdowns have never been proposed as a way to reduce overall death. As there's no vaccine, no cure and no way to eradicate the virus completely they can't do that. They can only push the eventual outcome forward in time, with the goal of avoiding hospital overload. Sweden's ICUs have never gone above 80% capacity, thus their strategy is de-facto successful when judged by the original justifications given in other countries.

Meanwhile, shutdowns are themselves deadly. People are told to stay away from hospitals and put in a state of fear; as a consequence some people die of other causes that could have been prevented. Additionally when the lockdowns end they face a huge backlog of operations and diagnostics that weren't done because they weren't considered as critical - some people won't get them in time and will die of treatable diseases, simply for lack of healthcare as the backlog is drained.

In the UK there's now an analysis suggesting 2000 additional people a week are dying of non-COVID related causes because of the lockdowns. There is talk of rationing of healthcare, due simply to all the delayed work and not due to COVID related load (of which there has been nearly none - overflow hospitals were hardly used).

It's likely that in Australia cases will start to tick up as it enters the winter season, but that by the time this happens, your political system will have learned from elsewhere and the reaction will be appropriately mild.