Australia's prime minister vowed to stamp out extremism on Thursday as the nation mourned the youngest victim of the Bondi Beach shooting, a 10-year-old girl remembered as "our little ray of sunshine".

Father-and-son gunmen are accused of firing into crowds at a beachside Jewish festival on Sunday evening, killing 15 in an onslaught authorities linked to "Islamic State ideology".

Prime Minister Anthony Albanese promised a sweeping crackdown to banish the "evil of antisemitism from our society", saying "Australians are shocked and angry. I am angry. It is clear we need to do more to combat this evil scourge."

This included new powers to target extremist preachers and to refuse or cancel visas for those who spread "hate and division".

Australia would develop a regime for listing organisations whose leaders engaged in hate speech, he said.

"Serious vilification" based on race would become a federal offence.

As the prime minister spoke, mourners gathered for the funeral of 10-year-old Matilda, the youngest victim slain in the attack.

"Matilda is our little ray of sunshine," said the rabbi leading the service, reading out a message from her school.

"She is genuinely the most kind, caring and compassionate young girl, who brightened everyone's day with her radiant smile and infectious laugh."

Black-clad mourners clutched bouquets of lilies as they filed into the funeral at Sydney's Chevra Kadisha, a Jewish society responsible for customary burial rites.

Others held balloons emblazoned with pictures of bumblebees, a reference to the young girl's nickname "Matilda Bee".

Matilda's family – who have asked media not to publish their last name – left Ukraine to settle in Australia before the Russian-Ukrainian conflict began.

"I couldn't imagine I would lose my daughter here. It's just a nightmare," mother Valentyna said ahead of the funeral.

Her father, Michael, said they chose her name as a nod to Australia, where the beloved folk song "Waltzing Matilda" is sung as an unofficial national anthem.

"So just remember. Remember her name." (AFP)