Dozens of protesters gathered outside the event on Wednesday at the City of Perth Library, held to celebrate the International Day Against Homophobia, Biphobia and Transphobia.
Images published by news website OUTinPerth showed one protester making a Nazi salute and brandishing a sign likening drag queens to pedophiles.
A small group of counter-protesters also attended the event which featured drag queen Cougar Morrison reading picture books to children.
The acclaimed performer has held the storytime activities for several years and was recently targeted before a similar event held by the City of Bayswater, with "hateful" flyers dropped in letterboxes in the area.
"It's just wild to me that you would take time out of your own day to protest against how someone else is raising their children," she said in an Instagram post after the City of Perth event.
Monash City Council in Melbourne cancelled a drag storytime event scheduled for the same day, citing threats of violence against staff, families and a performer.
Police briefed officials about safety risks after activists protested against the planned celebration at a council meeting last week.
A City of Perth spokeswoman said the event had been held three times at the library and received positive feedback.
"We remain committed to offering diverse and inclusive programs that serve the various interests of our community," she said.
All staff, including the presenters, were required to hold working with children checks.
Attendees were required to book tickets and children be accompanied by parents or guardians.
"The Drag Story Hour program is internationally recognised and incorporated into youth programming across numerous libraries worldwide," she said.
"This event encourages early literacy and a love of books whilst celebrating the differences that make us unique."
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