The impostors, a man and a woman, presented fake identification and told the mother they were conducting a welfare check, authorities said.
The woman later contacted authorities, who confirmed the visit was suspicious.
New South Wales authorities have issued a warning to the public.
The family had not had dealings with welfare authorities or police before the incident in Queanbeyan, near Canberra, last Friday, New South Wales Police said.
After arriving at the house, the impostors presented what appeared to be an identity card for the state Family and Community Services.
The mother told them her two infant children were asleep, and asked if they could return at another time. The pair said they would wait.
They later inspected the children and their bedroom, before leaving the home.
Welfare authorities confirmed that no visit had been scheduled, and reported the incident to police.
Chief Insp Neil Grey urged the public to vigilant, despite no reports of similar incidents in the area.
He said all welfare caseworkers carried photo identification showing their name, job title and an agency logo. (Courtesy BBC)