There are no "traditional" Christmas carols that have been written in Australia.
There are some popular and uniquely Australian songs, some of which have the word 'carol' in the title, such as:
you should now it you self
The Christmas song Jingle Bells.There are no songs that are Famous that were written in Australia, and furthermore "Jingle Bells" was without a doubt not written in Australia. The only Christmas song I know of that was written in Australia is called "Six White Boomers."
United Kingdom (England)
A Christmas Carol by Charles Dickens is written in English.
"A Christmas Carol" was written in England by Charles Dickens in 1843.
The surname of the author who wrote "A Christmas Carol" is Charles Dickens.
"Hark! The Herald Angels Sing" is a Christmas Carol written by Charles Wesley in 1739.
The Christmas Song by Mel Torme
The story was called A Christmas Carol and it was written in 1843.
Silent night
The united kingdom
It was written in 1843