Charley,
There is a rich lode concerning the colloquial meanings of "The Push" in Oz. While there were Oz military interpretations in WWI they had a backdrop of meanings as used earlier in both Sydney and Melbourne and celebrated in verse by both Lawson and C.J. Dennis.

Lawson is credited with authorship of the apocryphal "The Bastard from the Bush", a poem that has accumulated as many oral versions as Eskimo Nell (whose authorship is similarly obscured but credited to various poets of serious repute). Lawson did publish a very tame (by comparison) version, called "The Captain of the Push", which omits the most famous (probably) curse in Australian verse.

C.J. Dennis captured the lingo of the Melbourne versions of the pushes in his poems;
Er name's Doreen ...Well, spare me bloomin' days!
You could er knocked me down wiv 'arf a brick!
   Yes, me, that kids meself I know their ways,
   An' 'as a name for smoogin' in our click!
I just lines up 'an tips the saucy wink.
But strike! The way she piled on dawg! Yer'd think
   A bloke was givin' back-chat to the Queen....
      'Er name's Doreen.

"The Intro" from The Songs of a Sentimental Bloke by C.J. Dennis is just one example.

Cheers, Rowan