Is it time to give the royals the push?

That is the question that most Antipodeans are asking as, gaffes and scandal apart, they yawn their way through the Queen's visit

Wearing a hat that made her look as if she had a rose branch growing out of her head, the Queen listened po-faced yesterday as the Australian Prime Minister, John Howard, referred to her late father as King George V.

The slip had been corrected by the time a transcript of Mr Howard's speech was issued. But the incident, at the opening ceremony of the Commonwealth summit on Queensland's Sunshine Coast, summed up the flavour of the Queen's tour of Australia and New Zealand.

From the Duke of Edinburgh's latest gaffe – asking Aborigines whether they still threw spears at each other – to the embroilment of the Governor-General in a child abuse scandal, it has been an unfortunate start to a year of Golden Jubilee celebrations.

Instead of enthusing loyal Antipodean subjects, the trip has focused attention on the monarchy as a remote and increasingly archaic institution. "By the way, our head of state's in town next week," remarked The Australian newspaper as the Queen prepared to fly in.

New Zealand's Prime Minister, Helen Clark, was not even at home to greet her in the capital, Wellington, preferring to attend a conference of social democratic leaders in Stockholm. On her return, Ms Clark, who has described the monarchy as an irrelevance, horrified protocol-watchers by wearing trousers at a state dinner.

Mr Howard, one of the Queen's biggest fans, was at Adelaide airport to welcome her when she arrived wearing a suit variously described as lemon, mustard and apricot. But so, too, was the embarrassing figure of her Governor-General, Peter Hollingworth, stubbornly resisting calls to resign over his mishandling of a paedophilia scandal.

On her public outings, the monarch has met with polite indifference. In New Zealand, a few hundred people turned out to wave flags as she glided between Wellington, Christ-church and Auckland. Brian Rudman, a columnist with The New Zealand Herald, called her "a constitutional Santa Claus from another age". In the South Australian town of Elizabeth, named in her honour, 23 locals were waiting when she arrived by train. Tens of thousands greeted her when she visited the town in 1963.

Things were different then; nowadays the royal itinerary is almost a parody. On Thursday, for instance, the Queen began her day at the Adelaide Hills Kennel Club, where she confided to fellow corgi breeders that she recently bred two "tricolour" pups with black as well as red and white in their coats. She then proceeded to the town of Gawler, where she was serenaded by schoolchildren, and on to the Barossa Valley, South Australia's wine-growing region, where she planted a rose named after her and sampled a glass of Riesling. "She was very nice, a charming queen," commented one onlooker, Igor Moisseff.

It was confusion and fear of the unknown that made Australians vote to retain the Queen in a referendum two years ago; opinion polls consistently find a majority in favour of a republic. Although many remain fond of her, she arouses enthusiasm only among an ageing generation still convinced that it is living in a tropical outpost of Britain.

New Zealand has not yet grappled with the republican issue, but Ms Clark has said it is inevitable that the nation will one day cast off the monarchy. Across the Tasman Sea, the Hollingworth affair has highlighted the anachronistic role of the governor-general, the de facto head of state in the Queen's absence. He performs largely ceremonial duties on her behalf but can also dismiss the prime minister, as Gough Whitlam discovered in 1975.

The prime minister can also sack the governor-general, a power that Mr Howard has declined to exercise following claims that Dr Hollingworth mishandled cases of child sexual abuse by clergy and teachers when he was Anglican Archbishop of Brisbane in the 1990s.

Dr Hollingworth will wave off the Queen when she flies out of Brisbane today, concluding an underwhelming Antipodean tour that has done little to enhance the standing of the monarchy and may give republicans at home some food for thought.