Green’s Dictionary of Slang

(Aus.) to go on the tramp, carrying one’s pack; thus Matilda-waltzer n., a tramp.

1895		‘Banjo’ Paterson ‘Waltzing Matilda’ [song title].
1901		H. Lawson ‘The Romance of the Swag’ in Roderick (1972) 501: Travelling with the swag in Australia is variously and picturesquely described as ‘humping bluey’, ‘walking Matilda’, ‘humping Matilda’, ‘humping your drum’, ‘being on the wallaby’, ‘jabbing trotters’, and ‘tea and sugar burglaring.’.
1903		Bulletin (Sydney) 10 Dec. 38/1: ‘Want a job?’ / ‘We do thot, sorr. ’Tis fower wakes since we lift Amoy – Patsy an’ me – wid iligant chicks, be the same token. We waltzed Matilda into the township, an’ had the misforchune to fall in wid bad comp’ny – we’re taytotallers in a gin’ral way.’.
1924		Lawrence & Skinner Boy in Bush 249: If he’s got a pack, it’s his swag. If he’s only got a blanket and a billy, it’s his bluey and drum. And if he’s got nothing, it’s Waltzing Matilda.
1939		Age (Melbourne) 21 Jan. 11/8: A ‘swaggie’ waltzes ‘matilda’ carrying his ‘tucker’ in a sugar bag in one hand and his ‘billy’ in the other, while his faithful hound trails nonchalantly behind, wondering why life is life, and, what is what.
1941		Baker Popular Dict. Aus. Sl.
1955		N. Pulliam I Travelled a Lonely Land (1957) 241/2: waltz matilda – see hump the bluey.