The Department says it then plans to try and return the family to Papua New Guinea, a country through which they are believed to have travelled through on their way to Australia.
A man, woman and their son, aged nine, arrived by boat on Saibai Island on Sunday night, and have told immigration officials they are from Afghanistan.
The Immigration Department says if P-N-G won't accept the family, they would then be processed at an offshore detention centre such as the one on Nauru.
However Diane Hiles from ChilOut, Children Out of Detention, claims the department would be breaking Australian laws if it sent a child to a detention centre for processing.
“It was part of the changes that were made when all the children were let out of detention last July. The Migration Act then was altered to say children would not be detained, except as a matter of last resort. To my knowledge, despite the proposals that are before Parliament, the Migration Act has not been changed. So I'm at a loss to understand how they think this can be justified,” said Ms Hines.