Well my first try yielded a song from 1899 titled 'A FEDERAL SONG', music by George Sampson and words by George Essex .

"In the greyness of the morning we have seen the pilot star
In the whisper of the morning we have heard the years afar,
Shall we sleep and let them be
When they call to you and me?
Can we break the land asunder God has girdled with the sea?

Chorus For the flag is flying oer us, from the desert to the sea,
March shoulder firm together to the days that are to be;
The flag is flying o'er us and the Star of Hope we see,
Uplift the mighty chorus for Australian Unity!

There are two similarly uplifting verses which I won't transcribe for the moment. No mention of 'Australia(ns) True', hence very unlikely to be the song you seek.

For the sake of posterity 'A Federal Song' is notated in 6/8 in the key of D. Performance recommendation 'With Spirit'. (I think I'd need several to sing this one in public). The front page is adorned with a flag depicting the Union Jack placed in the top left quadrant of the Eureka Southern Cross - not too bad a look, except for the Union Jack.

I have a couple of other options yet to try. I'll be in touch.

Regards, John