Harper is one of the youngest patients to undergo the intense cancer treatment at the Children's Hospital at Westmead, and parents Katie and Luke are heartbroken.

The couple knew that there was every chance she would develop retinoblastoma - a childhood cancer of the eye - after genetic testing in utero revealed she had the RB1 gene.

Mr Rollinson, a town planner and partner in a Wollongong real estate firm, carries the gene and his right eye was removed due to a tumour when he was just 18 months old and replaced with a glass eye.

The couple's first-born, son Eli, was tested when he was six months old and a small tumour was discovered on his retina, which has been successfully treated with laser and cryotherapy.

Tests on Harper one week after her birth on November 26 revealed a large tumour in her right eye, which required far stronger treatment.

"Katie had an amniocentesis at 19 weeks to do some genetic testing to see if Harper had the RB1 gene - and she did," Mr Rollinson said.

"It's a very aggressive cancer so Harper was delivered early, at 37 weeks, so that she could be tested for a tumour as early as possible.

"Those tests showed that there was a very large tumour, which was too big for laser treatment and so we had to make some difficult decisions."

Under the advice of specialists, the couple decided to try to save the eye and so chemotherapy was the only option.

Initially, Harper will undergo three rounds of chemotherapy and if the tumour has shrunk significantly, then laser treatment can be used.

"Chemotherapy is not something you'd wish upon anyone - especially someone so small," Mr Rollinson said. "Hopefully, she'll be through this before she even remembers it."

Harper finished her first course of treatment a week ago and should be able to spend her first Christmas at home before the next round begins on December 30.

"When she was getting the chemotherapy she was fine but when we got home a week ago, she started getting really fussy, she wouldn't sleep and she fell below her birth weight," Mrs Rollinson said.

"She had to be admitted to Wollongong Hospital where she was tube-fed and gained some weight. She's doing much better now and we hope to keep her home for Christmas."

The Rollinsons have praised the staff at Westmead and Wollongong hospitals for the "amazing work" they do. They are also grateful for the support of other families with sick children they have met, as well as their own families and friends.

The kindness of a stranger has also touched them. Victorian mother Cassie Fersterer set up a GoFundMe page (gofundme.com/istzyk) to help the family with medical and related expenses - a page that has raised nearly $5000 in 10 days.