The death of Aishwarya Aswath at Perth Children's Hospital will be the subject of a coronial inquiry assisted by WA Police, Premier Mark McGowan has announced.

It is also being investigated by the Child and Adolescent Health Service.

Seven-year-old Aishwarya spent two hours waiting in the emergency department after presenting with a fever and being triaged in the second-least urgent category.

Aishwarya's parents had pleaded for her to be assessed by doctors after her eyes became cloudy and hands turned cold.

She died soon after she was finally seen.

Her death comes after months of concerns about understaffing, treatment delays and record ambulance ramping at Perth's hospitals, despite the re-elected Labor government having the benefit of a $3.1 billion budget surplus.

In his first public comments about the incident after being on leave this week, Mr McGowan said Aishwarya's family deserved answers.

"It's a very, very sad thing for the family. I think everyone feels for them but we can't possibly understand their grief," he told reporters on Friday.

"It's beyond imagining.

"There'll be two inquiries into the matter to get to the bottom of what has occurred. I think we owe the family and Aishwarya that as a state."

Mr McGowan declined to say whether he believed understaffing may have contributed to the incident, saying he would await the findings of the inquiry.

Four emergency doctors were off sick that night.

According to WA Health, there have been 21 "SAC 1" events - clinical incidents attributable to healthcare provision, or lack thereof, that could have caused serious harm or death - at Perth Children's Hospital since January 1, 2020.

That includes one patient who died and seven others who suffered serious harm. The rest suffered moderate or minor harm.

Aishwarya's death is yet to be classed as such an event.

Nurses had raised concerns about understaffing at the hospital months earlier and Health Minister Roger Cook has been slammed for failing to act on warnings from the sector.

The premier said Mr Cook was an outstanding minister but conceded hospitals were under strain and would require further investment.

"The system is under pressure," he said.

"That's why we are bringing on board all of these additional staff, all of these additional beds, new hospitals and rebuilt existing hospitals to deal with these situations.

"Clearly some of these things take some time but there are additional beds being brought on as a matter of urgency."

It's expected the report into Aishwarya's death will be finished in four weeks and be made publicly available.

Australian Associated Press