Green’s Dictionary of Slang

tommy v.1

[ety. unknown]

(Aus.) to leave.

[Aus]Williamstown Chron. (Vic.) 27 Apr. 8/1: Things are getting that hot in this year of dress, a mate of mine walked into a dance hall and ‘tommied’ out thinking he had made a mistake and entered a ladies’ dressing room.
[Aus]Baker Popular Dict. Aus. Sl.
[Aus]Truth (Sydney) 9 Dec. 7/5: ‘The fight lasted about 20 minutes. Kennedy then got away. He tommied off like a Bondi bus. Then I shot through,’ said Buttle.

In phrases

do a tommmy-off (v.)

(Aus. Und.) to leave quickly (under duress).

[Aus]Sun. Mail (Brisbane) 13 Nov. 20/8: ‘So-and-so strapped me for a shwe to-day. He was in a yike up north and copped a blue. Had to do a tommy-off and he is down here in smoke.’ Translated, someone had borrowed a florin from the speaker. He had got into trouble in the north and with a warrant issued for his arrest had escaped by boat and had gone into hiding.