I'm a bit hesitant about making any suggestions on this subject because I tend to treat these legends and songs with a lot more respect than I did a number of years ago. If you have heard a song about this, is it possible that it was a Rolf Harris creation? He was (probably) one of the first non-indigenous people to popularise songs of this type. While this is a pure guess, is it possible that 'Sun Arise' deals with this subject?

The first phrase - with a didgeradoo style monochord backing goes "Sun arise early in the morning".

Regards, John