It could have been the highpoint of the State visit - a showdown between the President, Mrs Mary McAleese, and the xenophobic Queensland MP, Ms Pauline Hanson.
An encounter might have breached protocol but it would have done wonders for a stodgy election campaign, especially when two such diametrically-differing personalities were in the same state.
They do have a few things in common. Both are proud of their Celtic traditions and came to fame from humble beginnings.
But the President and the leader of the anti-immigration One Nation movement differ markedly on such matters as the path to peace and reconciliation between different groups.
In 11 days on the road, 4,000 miles in the air and 39 speeches, Mrs McAleese spoke about little else. She banged the drum for Irish business and sang the praises of her State's cultural and economic renaissance.
But her most important message was not just how the peace process had survived and thrived. It was about the responsibility of each individual to share in the long-drawn-out process of putting together the building blocks to allow diverse groups to live together in open, international societies where each one's culture is respected.
The notion is perhaps a little esoteric for Ms Hanson, whose party aims at zero immigration and the end of alleged "special treatment" for Aborigines and the poorest of migrants. The independent MP has done little to provoke peace anywhere.
But it has struck home in a multicultural land which is groping to decide what sort of future and cultural identity it really wants: the inclusiveness of Mrs McAleese or the isolationism of Ms Hanson.
The President is not the only person articulating these ideas in Australia but she managed to impress them upon the thousands of people who have heard her speak with a determined passion.
She identified one of the highlights of her trip yesterday and it was not one of the stage-managed highlights such as the parliamentary luncheon with Prime Minister John Howard in Canberra.
It was the meeting with a man from Galway who, after 50 years, spoke with a rich accent of how he had gone to Alice Springs in the desert and, against the prevailing attitudes, married an Aboriginal woman.
He was one of the many "ordinary" people who waited to meet the President. His son is now the chief of an Aboriginal tribe and Mrs McAleese readily bundled him up with pride as a new addition to her grab-bag of the 70 million strong global Irish family.
"I'm delighted we have this Irish-Aboriginal link and that we can say in some shape or form these two cultures are fuelling each other and assisting each other to grow and develop," she said.
Tomorrow Ms Hanson will unveil her policy towards Aborigines and, to use an Australian expression, even Blind Freddy can see it will hold little generosity of spirit for the likes of the grandchildren of the man from Galway.
Mrs McAleese's visit did not attract screaming headlines, but she has planted seeds which, over time and with some tending, will grow.
She has also done wonders for the republic debate by showing just what a President can do when she has grace, humour and wit to bang the drum for her country with vigour. An abiding fear here is that a popularly elected President, such as Mrs McAleese, could get too big for their boots and somehow threaten the dated myth that Australia is a wholly egalitarian society.
But the President seemed to practise what she preached when she told this reporter that she remained true to the little girl she used to be with "patent leather shoes and a pointy-out skirt" growing up in Belfast.
"I'm one of nine kids and the other eight are great critics. I'm part of a family of 60 first cousins, all of whom are very close to each other. I think it's impossible to get above yourself in that kind of environment and that's what keeps you humble."
During this tour she has received the full red-carpet treatment, with motorcades and gala dinners galore, and the planting of trees and unveiling of plaques.
These are the routine events of State visits. But her legacy could be more out of the ordinary. The histrionic Ms Hanson may have got more column inches this week but Mrs McAleese left a more thoughtful and lasting, if less dramatic, impression.
They may never meet, but in this neck of the woods their battle will continue and many hope it will be common sense and not blind fear which prevails.