A young girl's appendix ruptured as she waited for hours in a crowded hospital emergency department in Adelaide, prompting an official investigation and an apology from the South Australian premier.

Annabelle and David Oates took their seven-year-old daughter Audrey to the Women's and Children's Hospital in March after their GP diagnosed her with acute appendicitis.

But they told reporters on Monday that she wasn't examined by a doctor for six hours and waited another two-and-a-half hours before an emergency operation was performed.

They also described how the emergency department was overcrowded with people standing in corridors with their children waiting to be seen.

Mrs Oates said she felt really sorry for the doctors, nurses and staff because there weren't enough of them to deal with the demand.

"Audrey was able to get the surgery even though there was a delay," she said.

"But you can imagine some family just turning away or not understanding things and you know their child could have died.

"I don't want that for anyone. I want the staff and the hospital to have the resources to be able to provide for the state of South Australia."

In a statement, the hospital said a senior clinician had been in contact with the family and apologised for the delay in treatment.

The hospital said an investigation into the circumstances surrounding the care of the child has been underway for several weeks.

Professor Warren Jones, a retired obstetrician and gynaecologist who has campaigned for better services at the Women's and Children's Hospital, said the case was a major dereliction of care in a system that was overloaded and dysfunctional.

Premier Steven Marshall said the situation was "not good enough" and offered a heartfelt apology to the young girl and her family.

"We've got to make sure that this situation doesn't occur again," he said.

"I do emphasise that our doctors and our nurses make decisions and they get it right the vast majority of times.

"In this instance, something has gone wrong and there will be a full investigation."

Mr Marshall said the government was already working to expand emergency departments across Adelaide with an emphasis on paediatric services.

He said plans were also underway to build a new children's hospital and investment in the existing site would continue to ensure it could offer the best possible services until the move to the new facility.