A six-year-old Canberra girl fighting cancer has undergone an Australian-first robotic surgery to remove a tumour which was initially considered inoperable.

Six-year-old Freyja Christiansen faced a grim prognosis when doctors found a tumour at the base of her neck, but Australian-first robotic surgery is being credited with a miracle.

The Canberra youngster was diagnosed with an aggressive form of cancer called clear-cell sarcoma in 2016 and she is thought to be the youngest of 40 cases ever recorded worldwide.

It was the position of Freyja's tumour, between a main artery and the base of her skull, that posed a problem for specialists who said the situation seemed hopeless.

The prognosis didn't stop Freyja's mother, Liz, and oncologist Antoinette Anazondo from searching for a cure.

"I was told my daughter's cancer was inoperable and incurable and that I couldn't can't even discuss options, I wasn't going to find a cure," Ms Christiansen told AAP.

"But Antionette would not give up and we spent the next year calling all around the world, researching possible treatments and then we learnt about robotic surgery."

Freyja began targeted immunotherapy last year, which was previously only available to adults, while the duo searched for a surgeon who would be willing operate using a machine called da Vinci which operates a small robotic arm.

Thirty-seven surgeons across the world refused to use the technology on Freyja.

"It was during a phone call to Boston Children's Hospital that the name of Melbourne cancer surgeon Ben Dixon came up," Ms Christiansen said.

"It was a bit of a fluke really ... we were willing to fly anywhere in the world but the fact that we had the skills and the technology in Melbourne was amazing."

On February 28, Epworth surgeons Ben Dixon and Matthew Magarey used the robot to successfully remove part of Freyja's tumour, with another surgery scheduled for Wednesday to remove a larger portion, dubbed the "big mama".

"I know there's a lot more to come, but to even get to this point, it's really been miracle after miracle," Ms Christiansen said.

"She shouldn't be here, but here she is."