The Queen watched a display of Aboriginal dancing
Dr Hollingworth greeted the Queen at Adelaide International Airport on Wednesday with a deep bow and a handshake.
The Queen and the Duke of Edinburgh's tour, which has included Jamaica and New Zealand, has already been dogged by opposition from republicans in the southern hemisphere.
Allegations against Dr Hollingworth relate to his handling of child sex claims against clergy in Queensland while he was the Anglican Archbishop of Brisbane in the 1990s.
Roving protest
The Queen and her husband, Prince Philip looked relaxed and chatted amiably with the governor-general as they met.
The Queen and Mr Hollingworth then spent 30 minutes in a private audience.
Asked earlier by a reporter if he had embarrassed the Queen, the governor-general replied: "We are very honoured to receive her in Australia."
He was at her side at a ceremonial welcome outside Government House in Adelaide city centre, where she was greeted by a crowd of about 15,000 people.
Protesters have pledged to follow Dr Hollingworth during the Royal visit but insist they are not targeting the Queen.
Edith Pringle, 42, armed with a placard reading "Resign Now - Zero Tolerance on Abuse", said: "We need a governor-general who is a social caretaker and a moral leader."
Another protester said white balloons he was carrying "symbolised child abuse survivors as a protest to try to force the governor-general to do the honourable thing and resign because of his complicity".
New allegations
Mr Hollingworth came under more pressure on Wednesday when he confirmed a report in The Australian newspaper that he once gave a character reference for an Anglican priest without mentioning sexual misconduct allegations against him.
The governor-general explained his action in a in a statement, saying the allegations were not proven at the time and he had assumed there would be a further request for further information.
Dr Hollingworth, backed by Australia's Prime Minister John Howard, has refused to resign.
But government officials in Canberra fear possible public protests against the governor-general could mar the five-day royal visit which includes the Commonwealth Heads of Government Meeting due to start on Saturday.
Mr Howard, who also greeted the Queen at Government House, said there had been nothing to alter his view that there were no grounds to dismiss Dr Hollingworth and that he would not change his decision.
The Queen and Prince Philip will return from their 15-day tour on 4 March.