The Queen will meet Prime Minister Julia Gillard at Government House for an informal discussion Friday, and it is going to be a private meeting.

The media has been passing on jokes that curtsying could not possibly be on the agenda, but many Australians have yet to get over the fact that Gillard preferred to shake the monarch's hand.

Talking to Neil Mitchell on radio 3AW, the prime minister said she merely did what she was comfortable doing.

"I felt most comfortable with bowing my head and the Queen extended her hand and so, of course, I shook her hand," Gillard said.

Asked whether she found curtsying demeaning, Gillard preferred to give an indirect answer.

"Some things are you, some things aren't. I made a choice and I thought I would feel most comfortable with bowing my head. The advice was to do what comes most comfortably and naturally."

No one could tell whether the Queen would discuss with Gillard her expressed preference for Australian republic -- after the monarch dies.

The Queen's strictly private meeting with Gillard will be followed by another closed door meeting, this time with Opposition Leader Tony Abbott.

Asked on what he thought about the scheduled meeting, Abbott seemed to anticipate sound advice from Queen Elizabeth II.

"The Queen has had almost 60 years on the throne," he told the Herald Sun. "She's seen opposition leaders and prime ministers come and go, if she wants to give me a little bit of her wisdom and experience I'll be very grateful to receive it."