Interesting lead worth repeating from above source:

Notes

First published in the Bulletin in 1892 This poem of Banjo Paterson's ('The Bushman's Song') has grown a number of tunes in its time in the bush. Meredith collected three tunes in NSW, and two tunes are given in the Queensland Centenary Pocket Songbook while in his Big Book of Australian Folk Song Ron Edwards gives another two. This tune is the one most commonly sung today, and was collected separately by Geoff Wills and John Manifold. Manifold got it from Mr Hines of Donald, Victoria, it is in his Penguin Australian Song Book

So there are a few questions:

1). Is the Bushman's song exactly the same at "Travelling..."? 2). What are the origins of the 3 tunes that Meredith collected? 3).What about those 2 tunes in the QCSB?