Cars have been spray painted with threats, she added.
Muslim leaders including the Grand Mufti of Australia Dr Ibrahim Abu Mohamed and Sheikh Yahya Safi, the imam of Lakemba mosque, have condemned "the horrors conducted overseas in the name of religion" as "crimes against humanity and sins against God".
"The recent so-called fatwa from overseas making reference to Australia as a target has no religious authority and must be rejected," they said.
Prime Minister Tony Abbott recently raised Australia's terror alert level from medium to high amid fears Australians returning from the battlefields of Syria and Iraq could pose a danger.
In the past week several counter-terrorism raids have been carried out in Sydney and Brisbane, while Parliament House in Canberra has beefed up its security.
"The sanctity of life is of paramount importance to all people of faith," the Muslim leaders said.
Samier Dandan, president of the Lebanese Muslim Association said anti-terrorism laws, being debated in parliament, needed to strike a balance between the need for safety and freedom.
"Our concern, first and foremost, is security, as long as it doesn't infringe of civil rights of any citizen of this country," he said.
Dr Abu Mohamed, Mr Dandan and Sheikh Yahya Safi on Wednesday met with Bishop Robert Rabbat of the Melkite Catholic Eparchy and other Christian leaders to promote peace and harmony in their communities.
The Islamophobia Register is a Facebook page set up by members of Australia's Muslim community to track religious hatred and discrimination.