If Lewis Carroll were able to peer through some weird looking-glass at today's Australia, he would likely have found himself rather tickled by Tony Abbott and Joe Hockey's recent use of language.

In Tony's Wonderland of Words, Julia is a liar (and Tony is not), promises are mere suggestions, debts are emergencies, cuts are subtractive increases and tax increases are levies, indexation adjustments, imposts or bracket shifts but never, ever, tax increases.

It is in this curious (and curious-er) environment that Australia prepares itself to once again celebrate the happy "un-birthday" of Queen Elizabeth II next week, on Monday 9th June.

The Queen's Birthday holiday is the cherry atop the towering Eton Mess of royal anachronism in which Australia still wallows, some 113 years after Federation.

Recognised annually on Australian soil since colonisation in 1788, it has been celebrated on the second Monday in June (since the death of King George V in 1936) in all states and territories except Western Australia.

Out west, the Governor of Western Australia rather randomly sets the Queen's Birthday holiday each year based on the dates of the Term 3 school holidays and that of the Royal Show.

It is not officially a national public holiday: it is a public holiday jointly celebrated by Australia's state and territory governments. Thanks to this antiquated historical convention, millions of Australians get a meaningless day off each year to go shopping, spend time with family and friends, take a "short break", play computer-games or binge on a DVD box-set, whilst pointedly not thinking about that grand old dame over 10,000 kilometres away, a dame who is definitely not thinking all that much about them.

The case for change is clear, but it’s bogged down in a quagmire of republican debate, culture wars, and the quintessential Australian fear that a public holiday could be taken away forever.

Regarding the republic, there is still a clear divide amongst Australians: most feel that Australia should have an Australian Head of State but remain reluctant to embrace ‘an Australian republic’, or are confused about what that would mean.

One could argue that it would make most sense to only alter the Queen's Birthday holiday convention in conjunction with the passing of a referendum that replaces the Queen with an Australian Head of State.

This line of argument is logical but flawed. Even if Australia were to remain a constitutional monarchy for the next 200 years, Australians would still be nonsensically obligated to take a day off work each year to not celebrate the non-birthday of a distant Head of State.

That some form of change makes sense is a reasonably open and shut case, but the question of how the Queen's Birthday public holiday should be changed remains vexatious.

Should it simply be abolished altogether? James Robertson has reported for the Sydney Morning Herald that the cost to the productivity of the NSW economy alone of a public holiday could be in the order of $800 million. Hardly pocket change in a period of national belt-tightening.

In the UK, the cost of a public holiday has been calculated by the Centre of Economics and Business Research as £2.3 billion. Contrastingly economist Andrew Leigh, the Federal Labor Member for Fraser, has argued that the economic cost of a public holiday is minimal, and generates valuable social capital for an already time-poor nation.

In any case, whatever the cost to the economy, it is difficult to imagine the average Australian welcoming the outright abolition of a public holiday with open arms.

The more politically palatable option is likely to be to introduce a new national public holiday to replace the Queen's Birthday holiday. Leigh also has some worthy suggestions on this front:

• Melbourne Cup Day (First Tuesday in November – already a Victorian public holiday)

• Remembrance Day (11th November – not currently a public holiday)

• Commemorating Sir Henry Parkes' Tenterfield Oration (24th October)

• Commemorating the Eureka Stockade (3rd December) Others options that have been suggested include: • Federation Day (1st January – an additional public holiday could be added to the New Year's period)

• Mabo Day (3rd June – commemorating the Mabo Indigenous land rights decision)

• Sorry Day (26th May – commemorating the National Apology to the Stolen Generations/Indigenous Australians)

Fundamentally the challenge for our nation would be to choose a new public occasion that can enrich the national consciousness, and which all Australians, regardless of their political leanings, could get behind.

As momentum grows – supported by both sides of politics – for Indigenous Australians to be recognised in the Australian Constitution, and in light of the pain that continues to be caused to Aboriginal Australia by the celebration of Australia Day ("Invasion Day"), there is a compelling case for the introduction of a new national day that is able to unite our first and later Australians.

Mabo Day or Sorry Day would be worthy options in an ideal world, but come with some political baggage for certain sub-sections of the Australian community. We need an event or person that everyone feels that can rally around, without reservation.

For example, a day that focused on reflecting on the Indigenous condition and commemorated the life of Aboriginal activist Mandawuy Yunupingu, the former frontman of Yothu Yindi (eg. "Mandawuy's Day" or "Treaty Day"), could provide a meaningful, apolitical focal point for the nation.

Yunupingu, born on 17th September 1956, passed away after suffering from advanced renal failure on 2nd June 2013. This was a life in which so much was achieved against the odds, but that was still tragically cut so short. A new public holiday at the start of June could feature as part of National Reconciliation Week, which currently is held between 27th May and 3rd June each year.

Extensive consultation would of course need to be undertaken with Aboriginal communities to determine whether referring to the name and images of the deceased Yothu Yindi singer would be acceptable in such a context, or best avoided altogether.

Australia could continue to not celebrate the un-birthday of a foreign Head of State, or we could celebrate the "legacy in progress" of an Indigenous Australian hero who broadcast native culture and issues across the airwaves and into the living rooms of Australia, and indeed across the world. It shouldn't be a very difficult choice to make.