If you had a penchant for punting, the good money is following Indigenous Affairs Minister Linda Burney into Yarralumla as the next Governor-General.

The symbolism in Australia’s first Aboriginal head of state would be strong; Burney replacing David Hurley as Governor-General would be a fitting recognition of Indigenous Australians in the wake of the Voice referendum.

Prime Minister Anthony Albanese is remaining tight-lipped, simply addressing the speculation by saying he had started consulting with the Palace, as required, ahead of Hurley’s term ending on July 1.

Other names are popping up too, including Indigenous leader and co-architect of the Voice Tom Calma – but it is the prospect that Labor Minister Burney will take the top job that is drawing the most attention from friends and foes.

Would Burney be the best person for the job? Former speaker of the house Bronwyn Bishop doesn’t think so. Neither does Deputy Prime Minister Barnaby Joyce.

The appointment of a politician to the role – despite the fact that Bill Hayden, for example, did a stellar job as Australia’s governor-general from 1989 to 1996 – will always bring criticism of partisanship.

Indeed, the Opposition’s Indigenous Australians spokeswoman Jacinta Nampijinpa Price believes race should not be considered in the appointment.

But if we did appoint an Indigenous Australian, perhaps Burney would be a fabulous representative for a modern united nation?

Professor Calma has strong support, but has been very public in pushing for an Indigenous Governor-General which, some say, lessens his chances. It shouldn’t.

Other names raised also include Ken Wyatt, Marcia Langton and Pat Dodson.

Barnaby Joyce has suggested rugby great Mark Ella as an alternative.

Or what about another non-politician, like Adam Goodes, for example – not on the back of his AFL record, but his commitment to the nation’s Indigenous youth.

He’s already been Australian or the Year. Or Cathy Freeman, who truly united the nation, during her historic run at the 2000 Olympic Games. Imagine her opening our next Games, in Brisbane in 2032.

But if the government chooses, in the end, not to appoint an Indigenous Australian, who might also help unite us, and show us off to the rest of the world?

Chris Hemsworth would certainly get our attention, but board shorts and a surfboard are probably not the Yarralumla look in 2024.

Paul Hogan, too, probably comes in as one prawn short of a barbie in what we expect from our Governor-General.

But Hugh Jackman would certainly sing and dance his way around the Governor-General’s residence, and be a widely popular choice too.

Just imagine if we took another road. The Governor-General doesn’t need to be a top military officer or expert in constitutional law. It needs to be a person who will make something of the job, for the rest of us.

So why not consider someone who would draw attention to science, and put a new focus on research?

Consider the broad coverage given to melanoma research, thanks to Professor Georgina Long and Professor Richard Scolyer, the 2024 Australians of the Year. In a few minutes, their award speech prompted an upswing in both skin checks and donations for further research.

A glance through previous Australians of the Year raises a dozen other names, including Professor Ian Frazer, who is behind the development of the cervical cancer vaccine – which now saves millions of people around the globe.

Ita Buttrose might have been a frontrunner once, but her stint at the ABC probably rules her out.

If you wanted to focus on the nation’s educational future, University of Sydney vice-chancellor Mark Scott would be in the mix – but his wife Dr Briony Scott, an educator for decades, is probably a notch above him.

Or we could showcase diversity, with Dylan Alcott. The heart and soul of our nation with Maggie Beer. Imagine the grounds of Yarralumla full with organic vegetables and its own YouTube channel of how we could grow them, with recipes to match. The possibilities there are endless.

Certainly, it would be a mighty step up from MAFS and the reality TV we have on offer now.

We need someone to unite us; to build a bridge from the past to the future, and who will showcase Australia both to those who live here and across the globe.

For my money, and if Albanese chooses to avoid the appointment of an Indigenous Governor-General, then Glenn McGrath should be in the mix.

He’s represented Australia in the baggy green as one of the greatest bowlers of all time, and has shown the nation how a baggy pink can be even more powerful; a uniting force on its own.

Devoted to helping women across the nation suffering from breast cancer, he’s as home in the outback as much as he is in the corporate boardrooms of Sydney and Melbourne.

He speaks (and presumably thinks) like the rest of us. A father bringing up a blended family. Married twice, he lost his first wife, Jane, too early. His second wife, Sara Leonardi, is Italian but now calls Australia home.

The Governor-General’s 54-hectare residence at Yarralumla would be a fitting backyard to play cricket in.