A 37-year-old female passenger was charged with possession of utensils for smoking methamphetamine.
A Whangarei police officer said the car was impounded and arrangements made for the child to be picked up by a relative from the Far North.
"There's a huge volume of traffic out there and a majority of drivers are well-behaved who've been let down by some idiots caught speeding and making bad decisions," the officer said. "Be aware that your actions have consequences."
Another driving incident on Northland roads involved a male motorcyclist who was clocked by a police radar doing 124km/h on State Highway 1 in Uretiti about 8.50am on Christmas Day.
A chase ensued and he allegedly reached speeds in excess of 160km/h while overtaking traffic on double yellow lines.
Sergeant Grant Rouse said the 22-year-old motorcyclist was located at a house on Port Marsden Highway after the homeowner reported him pulling into the driveway. He is facing charges of reckless driving and failing to stop.
Some drivers have been clocked at 40km/h above the speed limit on the Brynderwyn Hills since Christmas Day.
