Shinia had started the school this year.
Her father and mother, Hine Minarapa, said they were "barely holding in there" as they tried to cope with the unexpected death of their little girl.
An unnamed relative told Fairfax the couple were "not good".
"The school is right there where the accident happened. We've been complaining for years, for a very long time, that it's 70km/h."
The council's chief executive Garry Poole told Fairfax he would "investigate this situation immediately".
Shinia was struck around 1.20pm yesterday, while out with her cousin. The driver of the 4x4 utility vehicle attempted to save the child.
The driver was last night assisting police with their enquiries.
Yesterday, neighbours who gathered at the scene were solemn. One said they heard a bang from inside her property when the crash happened, but had no idea what it could have been at the time.
They said the girl had come riding out of Waikare Rd onto Matapihi Rd where the ute hit her.
Her pink bike with white wheels lay smashed on the pavement just metres from their front gate.
"It's a very sad day," another neighbour said.