"Mum and dad were both home," Mr Shields said. "There was nothing sinister. It was just an unfortunate accident."
Mr Shields said he understood the girl would probably be released from Starship next week.
The clinical director of the children's emergency department at Starship Hospital, Michael Shepherd, said it was not unusual for Starship to see preschoolers who had a fall greater than 2m at least once a week.
Dr Shepherd said preschool-aged children were at a greater risk of falls because they did not understand the dangers of exploring high areas.
Subsequent injuries could be serious, including long-term brain injury, or could result in death.
Children and adults did not experience falls differently, but proportionate to their total size. Children had larger heads and were less inclined to put their hands out to protect themselves. This meant a potentially greater risk of brain injury.
Dr Shepherd said falls in the home were preventable and he believed landlords and families had a joint responsibility to provide a safe home for children.
This included putting stays on windows and gates at the top of stairs.
