"It's highly dangerous," Dr Galtry said. "I'm all for breastfeeding but not while driving a car."
Dr Galtry said mothers could not have babies dangling in mid-air while breastfeeding.
"You have to be holding some part of the baby."
Galtry said the woman would have been driving awkwardly, probably with one hand.
She advised frustrated mothers with screaming babies to pull over and stop the car in a safe place before breastfeeding.
Dr Galtry said it was also dangerous for passengers in a moving vehicle to breastfeed.
"If you're sitting in the passenger seat and you've got a screaming baby, I can imagine the temptation, but I mean, really."
Sergeant John Fagan told NewstalkZB police knew the woman's car registration number.
Dr Galtry said the incident was highly unusual.
In 2009, a woman in Ohio in the US faced charges of child endangerment after breastfeeding her baby and talking on her cellphone while driving.