Jessica Mostyn, 32, and her four-year-old son left a property in Labrador just before 5pm on Saturday after an argument with a person known to them, police said.
Jessica does not have a phone or car so police believe she is likely to reach out to the public for help.
“Jessica is unlikely to see this message, but if she does I want her to know she is not in trouble and we just want to check on her and her son to make sure they are okay,” Acting Detective Inspector Greg Aubort said.
“She is urged to come forward to a hospital or police station for help and I know our community here will guide her appropriately if she approaches them.”
He said Jessica’s family and loved ones share their concerns and want to see the pair home safely.
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“This appeal is all about making sure she and her son are safe – especially with the heavy rains and damp conditions we’re experiencing here,” he said.
Jessica has a fully shaved head but is known to wear a variety of wigs. She was last seen wearing a blue hoodie with maroon sweat pants.
She is described as Caucasian, 164cm tall, with a medium build.
Her son is described as Caucasian with blonde hair and blue eyes last seen wearing blue and orange shorts with no shirt or shoes.