To abscond, or depart quickly.
Bondi trams seem to be the favourite vehicle that Australians say 'shoot through'.
This expression is commonplace in Australia and New Zealand and is becoming more used elsewhere due to the influence of Australian soap-operas like Neighbours and Home and Away.
The first record I can find of it in print is a definition in the Australian pin-up magazine Pix, which was published in Sydney in September 1947 by Associated Newspapers Limited:
"Shoot through, escape, abscond."
For a popular magazine to have felt the need to define the expression it couldn't have been very old at that date.