Australia agreed in September to take in an extra 12,000 refugees amid public pressure over Europe`s migrant crisis.
The first Syrian refugees had not expected to arrive until December.
Federal Minister for Social Services Christian Porter said the family had "been through a great deal".
They had spent very long periods of time in refugee camps as a result of the Syrian conflict, a spokesperson for the minister told the BBC.
`Intense` testing
Foreign Minister Julie Bishop said all those being given refugee status in Australia had been "handpicked" by authorities and faced a rigorous screening process.
She was responding to questions about unconfirmed reports one of the men involved in the Paris attacks on Friday had posed as a Syrian refugee to enter Europe.
"We are focusing on people who have been persecuted in Syria and Iraq, people who are fleeing from terrorism, from persecution. Our screening and testing is very intense," she told the Seven Network.
"Australia is in control of the whole process. These are not people who are coming via the people smuggling trade and we don`t know who they are."
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