Shoot Through Meaning

(Australia, New Zealand, informal) To leave.

Example: Used other than as an idiom: see shoot,‎ through.
1977, Valmai Phillips, Romance of Australian Lighthouses, unidentified page,
  He did not mind the new store, but when some stirrer said that there was a motel coming, he shot through to find a better hole further inland, muttering that 'the place is getting as big as one of them southern city places!’
1982, James K. Baxter, Howard McNaughton. Collected Plays, page 123,
  He shoots through to Australia, and I'm left with the kid.
2008, Elizabeth Bruce, A Show Off, Just Like Your Father, page 68,
  But on learning it was twins he shot through to Queensland into – I later discovered – the waiting arms of his lover.
2010, Stephen Lacey, Henry Loves Jazz: The Diary of a Reluctant Father, unnumbered page,
  What Father Nelson must have made of our all-too-candid (and slightly embellished) responses is anybody's guess, but it wasn't long before he shot through to New Guinea to work as a missionary with the kind of tribesmen who wear penis gourds.