The couple – no longer working royals and visiting in a private capacity – are combining visits to charitable causes with commercial ventures.
It is understood Meghan is exploring the Australian expansion of her As Ever lifestyle brand during the trip.
Later on Wednesday, the Duke will be in the capital, Canberra.
In Melbourne, Harry was special guest at the launch of a report into the mental health of fathers of young children, produced by the charity Movember.
After introducing himself with a “G’day everyone” and a brief reference to the Bulldogs’ promising start to the season, the Duke talked openly about his own mental health after becoming a dad – with references to his father, King Charles III.
“The world around us has changed massively, so there is no version of where parenting is going to be the same as we experienced,” he said.
“I see parenting evolving all the time. From my perspective, our kids are our upgrades.
“That’s not how I was taught, but that was my take on it. Not to say I was an upgrade of my dad or that my kids are an upgrade of me.
“That’s the approach that I take, to know that with the world the way that it goes, the kids that we bring up in today’s world need to be an upgrade.”
“Even if you had the best upbringing in the world, the best parenting in the world, there’s still room for improvement,” he added.
He also reiterated the importance of dads reaching out for help if they were struggling.
“For so many years it has been seen as a weakness to stick your hands up. I find it’s the opposite. The more grief I get for talking about it , the more I want to stand up and talk about it. I know if I go quiet about it – what does that say to everyone else?”