The duchess was offered a posy from 22-month-old Elizabeth Colquhoun, who then decided she wanted to keep the bouquet and refused to hand it over.
Camilla was visiting Perth's state library on the final day of the royal tour of Australia and New Zealand.
Elizabeth's mother Chantelle Colquhoun said her daughter was "strong willed".
Originally from the Cornish town of Camborne, Mrs Colquhoun, 39, was in a fit of giggles at her daughter's antics and said she was "just the same way at home".
The Duchess of Cornwall eventually managed to take the bouquet from Elizabeth and playfully held it just out of the grasp of the youngster until she grabbed it.
The duchess was at a book reading session at the time.
Meanwhile, the Prince of Wales was given a tour of a conservation centre.
He met students at the Western Australia Seed Technology Centre in Perth after attending a service at St George's Cathedral in the city with the duchess.
The royal couple have spent 12 days touring Australia and New Zealand.
Prince Charles celebrated his 67th birthday on Saturday with an Australian beach barbecue at Cottlesloe beach in Perth where he was joined by 500 guests.

The Royal College of General Practitioners (RCGP) said the figure had fallen to 351 from 366 in 2004/05.
In the same period, the number of registered patients rose by more than 125,000 to 1.92 million - an average increase per surgery of more than 500.
The RCGP said Northern Ireland had the lowest number of GPs per patient in the UK; a shortfall equating to 234 GPs.
RCGP chairman Dr John O'Kelly said: "With growing numbers of patients, and fewer GP surgeries, general practice is creaking at the seams.
"But this pressure and the danger it poses to our patients has not yet been adequately recognised by decision makers.
"Whilst other countries in the UK are being promised increased resources to cope with increasing patient demand, in NI - where our patients already have fewer GPs per head - general practice has largely been ignored."
Northern Ireland has been allocated about Â£41m in additional public spending next year.
This is Stormont's share of the extra Â£2bn allocated to the UK health service by Chancellor George Osborne in his Autumn Statement.
However, the Northern Ireland Executive is not obliged to spend the extra money on health.
Dr O'Kelly said the money should be used to invest in stronger local GP services.
"To gain parity with other UK nations, we urgently need a package of measures to encourage more young doctors to enter the GP workforce, retain and support current GPs, and make it easier for those who have left the workforce to come back," he said.

Jayne Hickey, 30, and her son Christian, now aged eight, were both shot in the leg when two men knocked on their front door in Salford.
Police said both are continuing to recover after numerous operations.
The shootings were linked to armed gang feuds in the city including the murder of Salford's "Mr Big" Paul Massey.
Two men knocked at the door of the Hickey's family home on Gillingham Road in Eccles on October 12 last year and after reportedly asking for the boy's father, they fired shots.
The men were then seen speeding away from nearby Dover Street in a black Audi S3 shortly afterwards.
Det Ch Insp Howard Millington said: "Christian and Jayne are recovering well but what happened to them will affect them for the rest of their lives and we are determined to bring them justice."
He said officers want to speak to a youngster on a motorbike the offenders passed in the Audi on Worsley Road.
The men "drove at high speed" close to the rider, "causing him to pull over".
Officers are also trying to trace the occupants of a small dark-coloured hatchback saloon which had a broad stripe running diagonally from the front door over the wheel arches, that the Audi also passed.
The first offender is around 19 or 20 years old, of a "chunky" build and with a Salford accent, while the second man is only described as white. Both were wearing baseball caps.
So far 18 arrests have been made over the feuds between organised crime gangs in Salford. However, no arrests have been made over the murder of Mr Massey, who was shot dead outside his home last July.
The Duchess of Cornwall found herself in a playful tug of war with a little girl determined to hang onto her bunch of flowers.
[NEXT_CONCEPT]
The number of GP surgeries in Northern Ireland at its lowest since 1991, a group of doctors has said.
[NEXT_CONCEPT]
A renewed appeal to find the men who shot a seven-year-old boy and his mother on their doorstep a year ago has been launched.