Police would wait for an update on the girl's condition before deciding on any charges.
The driver was aged in her 80s.
Ms Beckett said it was a reminder for drivers to be extra vigilant as children returned to school after the holidays, and to observe the 40km/h speed limit around schools when children were present.
Pedestrians also had to be cautious when using crossings. Though they were in the right when using a crossing, it did not make them any safer or less vulnerable.
A St John spokesman said the girl, who was knocked unconscious, was due to have a CT scan yesterday to check for skull fractures or bleeding on the brain. It was hoped she had only suffered serious concussion.
Her condition improved en route and was described as moderate by the time she reached hospital.
Members of the public trained in first aid were quick to arrive at the scene yesterday morning. Others turned back traffic in both directions.
An elderly woman, seated on a school chair next to a Suzuki Swift with police paint marking its position, was seen being comforted by bystanders.