Several thousand women and men joined the movement in central Sydney and a similar number turned out in Melbourne.
Several thousand women and men joined the movement in central Sydney and a similar number turned out in Melbourne, AFP reporters said.
Hundreds also demonstrated in New Zealand's capital Wellington as well as in Auckland at the start of a day that will culminate with marches in Washington, where more than 200,000 are expected, and across dozens of US cities.
Organisers say more than 600 coordinated protests will take place around the world in defence of women's rights and against hatred and bigotry following Trump's inauguration.
Anti-Trump demonstrations in downtown Washington erupted in violence on Friday when more than 200 people were arrested for vandalism.
But there were no reports of trouble Down Under where Women's March organisers had called for a peaceful protest.
"Hatred, hate speech, bigotry, discrimination, prejudicial policies -- these are not American problems, these are global problems," Women's March Sydney co-founder Mindy Freiband told the crowd.
Under Sydney's summer sun there were not too many sporting the pink "pussyhats" -- woolly hats with cat ears -- that have become a symbol of the Women's March movement.
They are a play on the words "pussycat" and "pussy" in a bid to claim back the derogatory term for female genitalia that Trump used about groping women in a leaked tape.
Marchers say they want to vent against an incoming administration they fear will roll back women's rights. Australians said they felt equally worried, but not just about women.
"We are not just concerned about women, we think there are a lot of people threatened by these types of policies," Freiband told AFP.
"We also have people concerned about the treatment of refugees, detainees, aboriginal rights, science denial, global warming. These are universal issues".
Protester Emily Richardson hit out at Trump's sexual attitude towards women.
"I think that he is such a public figure, and everything he stands for, the comments that he has made and the attitude he has shown, it makes people think it is OK, it condones sexual assault.
"We can't have a figure in one of the biggest nations in the world say that these things are OK, because it allows everyone else to go further with those attitudes. It exacerbates everything," she told AFP.
Rachel Shaw said she feared for her child's future.
"I came here today because I want my daughter to know that she should be empowered as a woman," Shaw said.
"She has equal rights to men and... the right to protest about her rights... and do what she wants to do in life."