Stefanovic said the 'sex swap' wouldn't take place until the child is much older.
"Nothing happens in terms of surgery until 18... but there's counselling that starts at this point, then there's puberty blockers before puberty starts," he said.
"It's very private I believe."
Stefanovic was speaking to 3AW's Neil Mitchell at the time. Mitchell said he had changed his opinion of gender dysphoria after speaking with parents.
"I didn't like it, I thought how can a kid that age understand it? Then I got parents calling me whose children had been through it, some saw the signs at age three and four and by age seven and eight they were transitioning," he said.
The Westmead Children's Hospital in Sydney has had referral patients at its gender service department triple.
Child psychologist Michael Carr-Gregg said 250 children - some as young as three - have made appointments with the gender dysphoria unit at Melbourne's Royal Children's Hospital.
"I think there's some confusion over what transition means, transition doesn't mean a sex change, it means that they live ostensibly as the gender they want," Dr Carr-Gregg told Seven's Sunrise.
"If they are a little boy and they want to be a little girl they dress as little girls, they grow their hair long, they are called by another name, it doesn't actually meant that they get any medical intervention, that's something that they may or may not do as they grow older as puberty approaches."