Green’s Dictionary of Slang

(Aus.) goodbye.

1910		Bulletin (Sydney) 24 Nov. 30/2: I’ll vote for Mr. Wade if I git the job. Well, Tooraladi. P.s.: Put in a notis to the readers to send round to The Bulletin any ole boots. I will git them on me way home.
1916		Truth (Sydney) 23 Jan. 10/5: Page said, ‘Well, too-ra-loo; I’m getting off here.’ ‘Hoo-roo, Page,’ he replied [AND].
1927		Bulletin (Sydney)12 May 27/3: A man from Windsor (N.S.W.) parting from me a few days ago, said, ‘Well, tooroo – see you in Liverpool.’ Thirty years ago, ‘tooroo’ or ‘tooraloo’ was commonly used about Sydney. The expression seems to have come from the chorus of a then popular song, commencing ‘If I had the wings of a turtle-dove’, the last line being ‘I tooral looral I ay.’.
1942		A.L. Haskell Waltzing Matilda 38: ‘S’long Bill.’ ‘Too roo, Joe.’.
1948		J.K. Ewers For Heroes to live In 3: ‘Oh, well! Too-roo!’ He touched Darkie’s flank with his heel, gave a wave to both girls and was soon out of sight.
1964		North Aus. Monthly Dec. 8: We [...] swapped any news, the petrol tanks were ‘topped up’ and with a cheery ‘Too-roo’ we were off again [AND].
1970		(con. 1941) R. Beilby No Medals for Aphrodite 273: He had never been much of a one for good-byes. ‘Tooroo, I’ll be seeing you, be good,’ had always seemed quite adequate.
1984		Partridge DSUE (8th edn).