Whoops dyslexic finger.
I've found that Australian "Christmas Carol" list and it is below.

Coffs Coast Christmas Carols

From the Coffs Coast Advocate 16th December 2017

The First Noel
Run Run Rudolph
O Holy Night
Jingle Bell Rock
Rudolph the Red-Nosed Reindeer
Away in a Manger
Have Yourself a Merry Little Christmas
Santa Claus is Coming to Town
Jingle Bells
O come, o come, Emmanuel
Silent Night
O Come all ye Faithful
What Child Is This?
Six White Boomers
Rocking Around the Christmas Tree
Little Drummer Boy
We Wish You A Merry Christmas