The mother of a newborn baby who died in a Sydney hospital has been told she may not be able to claim compensation unless she can prove her emotional trauma amounts to a "psychiatric illness".

Youssef and Sonya Ghanem's son died on July 13 after he was accidently given nitrous oxide instead of oxygen at Bankstown-Lidcombe Hospital.

In June a girl born in the same hospital was left with permanent brain damage after she was also treated with the gas.

Under Australian law parents of children who die as a result of negligence are not entitled to any compensation unless they can prove they suffered from a psychiatric illness as a result of the death.

Professor of law at the University of Sydney, Barbara McDonald said the law represented a serious "gap" in the system.

"I think it's a great defect in our law that our Compensation to Relatives Act doesn't have any provision for bereavement damages," she told the Sydney Morning Herald .

"It is a really important gap in our law that we should remedy."

Given the severity and high profile nature of the Ghanem's case, Health Minister Jillian Skinner said the state government would "consider how best to continue to provide support to both families in the future, including the provision of monetary payments".

"(Payments) could be considered without the need for formal litigation", Mrs Skinner said.

Head of legal firm Maurice Blackburn's medical negligence practice, Libby Brookes said there should be special exemptions made to compensation laws.

"In this type of case, which is publicised and is so horrific, I'm sure that NSW Health will make it easy," Ms Brookes told Fairfax Media.