Hi Kirsty, I'm assuming you have already looked at the well-known songs that people have suggested. I found one that I'd never heard of before in a book 'Folk Songs of Australia' by John Meredith and Hugh Anderson called "The Bright Shades of Blue"

We had sailed in a vessel from Britain's cold shore;
I was treated unkindly, great chains that I wore.
My cares they were many, my joys they were few -
I'd left all my joys in those bright shades of blue.

Fair land of beauty, Australia so true,
How I sigh for those mountains in the bright shades of blue.
How well I remember that darkie's old song
That we sang round the fire, a once happy throng.

We had sailed in a vessel for Britain's brave shore;
I was treated with kindness,great jewels I wore.
But my cares they were many, my joys they were few -
I'd left all my joys in those bright shades of blue.

Fair land of beauty, Australia so true,
How I sigh for those mountains in the bright shades of blue.
Now I'm old and I'm feeble and my locks they are grey,
And the nearest and dearest will soon fade away.

When I'm dead in my grave all I want you to do
Is plant me a gumtree from the bright shades of blue.
Fair land of beauty, Australia so true,
How I sigh for those mountains in the bright shades of blue.

The book says that this was sung by Cyril Ticehurst of Kogarah Bay (no date given) and Sally Sloane (born 1894 in Parkes).

Good luck with your search,

Regards

Quokka