Year 4 student Mariam Issmail was in a nearby classroom when the SUV ploughed into the school.
It is not yet been established whether or not she had any connection to the school.
After the accident, two children are in cardiac arrest, another is in a serious condition, and two others are being treated for minor injuries.
The 52-year-old woman driver has reportedly asked for forgiveness.
Police said they believed the crash was not deliberate.
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Police established a crime scene and Ms Al-Shennag was later charged with two counts of risky driving occasioning death and one count of negligent driving.
"Obviously they were crying, they were distressed, some were asking for their parents, that's a natural response in such a awful set of circumstances".
The school will be open on Wednesday with support from counsellors for any student who wishes to attend, staff said on the school's Facebook page. Seventeen children and a female teacher were assessed on the grounds by paramedics.
"We are not looking at this as an intentional act", he said.
Dozens of parents frantically searched for information at police barricades as roads around the school were closed down throughout Tuesday.
The road has been blocked, but one parent of each child is being allowed to approach the school gate as police try to control crowds at the chaotic scene. "It is a crash investigation", Mr Smith said.
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