She went on: "There's a lot of Australian research that has actually informed a lot of international research ... that has demonstrated children's capacity to be really inclusive once they know about these ideas and they think, 'Wow, why are people seeing this as a controversy?"
Dr Scarlet, who insisted that was her real name, said that many families without fathers supported the idea.
"We have single parent families, satellite families, extended families, lesbian and gay families," she said.
Her ideas were met with a stern rebuke from New South Wales Liberal minister David Elliott, who called them "rubbish".
"Can't believe that someone who professes to be 'enlightened' would advocate such crap," Mr Elliott wrote on Facebook.
"People still celebrate fatherhood even after their father and grandfathers have passed away, in fact for many people Father's Day is a wonderful time of reflecting and remembering."
He went on: "Dr Red Ruby Scarlet - you are the offensive one. Maybe we should start a campaign to address that."
