I often get asked this very question by couples who wish to have a wedding ceremony in a foreign country where only a few friends and family can afford to go and wish to get married here again to share the moment with others.
I had one couple say to me it was ok to marry twice because she saw it on the internet. Unfortunately we can not believe every thing we find on the internet.

Marriage Act 1961 issued by the Australian Government . Guidelines for Marriage Celebrants
Section 9 Foreign Marriages.

LEGAL RECOGNITION OF FOREIGN MARRIAGES IN AUSTRALIA.
Part VA of the Marriage Act deals with the recognition in Australia of marriages entered into outside Australia under foreign laws. In general, if the marriage is recognised as VALID UNDER THE LAW of the country in which it was entered into, at the time when it was entered into, the marriage WILL BE RECOGNISED IN AUSTRALIA as a VALID marriage. This is the case whether or not the marriage involves Australian or non – Australian citizens.

The Marriage Act does not provide for overseas marriages to be registered in Australia. Whether an overseas marriage is recognised as valid in Australia is determined by the Marriage Act.

Wow so much jargon. In simple terms if you marry in Fiji, Thailand, England etc ,you are married under Australian law.
On the Notice of Intended Marriage form ,Question 5 asks Conjugal Status. ( never validly married, divorced, widower.
The above will clarify the rules for the vast majority of people.

Yes there are exceptions to the recognition of foreign marriages. Being valid in Australia.