The parents of the baby girl who suffered brain damage after a western Sydney hospital mistakenly administered a dangerous gas shortly after her birth, say they are devastated.

Danial and Benish Khan say baby Amelia suffered irreversible brain damage after being given nitrous oxide instead of oxygen after her birth at Bankstown- Lidcombe Hospital in June.

"It's devastating as a parent to be told that your precious daughter has suffered permanent brain damage," they said in a statement on Tuesday.

Amelia, their first child, has constant seizures because of the injury and requires a high level of constant care.

"We remain full of hope for Amelia's future but we worry for her and want to do everything we can to make sure she has the best life she possibly can," the Khans said.

"She will always have to live with the consequences of what was done to her at the hospital."

"But we will always be by her side and we'll do everything we can to give her the best possible future."

Mr and Ms Khan expressed sympathy to the Ghanem family, whose newborn son, John, was also administered nitrous oxide at the same hospital, and died in July.

"We can only imagine the intense pain this family is going through and our hearts go out to them."

A report found "a series of tragic errors" including incorrect installations of gas pipelines, flawed testings and significant clinical and management failures caused the deadly error.

Libby Brookes from law firm Maurice Blackburn is representing Mr and Mrs Khan and said Amelia's injury sustained at the hospital has had a "shattering impact on her parents and extended family".

"Like all parents, they were simply looking forward to welcoming their child safely into the world. Now their lives have been turned completely upside down," Ms Brookes said.

She is pursuing a claim for compensation on behalf of Amelia and her parents.

NSW Health Minister Jillian Skinner has faced torrid questioning over her handling of the gas scandal since it emerged in July.

Premier Mike Baird says compensation is being fast-tracked.

Mr Baird said the government is doing everything possible to support the couple.

"We will expedite anything we can and certainly that's what we are doing at the moment ... we (want to) take as much stress off as we can," Mr Baird told reporters on Tuesday.