Okay, here's what I was driving at with "Click Go the Shears".

It's in the lydian/major hexatonic mode (the fourth only occurs as an inessential passing note, if you sing it at all). There are a LOT of tunes in that mode in folk song from the British Isles. But there's more to it than that. Most of the notes in the scale only occur on falling phrases; this is common in Indian ragas (like Desh) but not so common in songs from Western Europe. The scale used for rising phrases is very minimal indeed. Basically the tune progresses by quick scrambles upwards and then a slower fall through narrower intervals over quite a wide range. This melodic shape is found all over the world, but it's more typical of technologically primitive societies like aboriginal Australia. The tune is also rather unusual in resolving to a tonal centre near the top of its range instead of an octave lower as you might expect.

I've only heard it in NZ - I'll take your word for it that the song is Australian, but the tune is presumably English.

Musically useful modal systems take account of gaps, scale asymmetries and melodic shape.