Green’s Dictionary of Slang

(Aus.) to live by oneself in a remote area.

1901		H. Lawson ‘That Pretty Girl on the Army’ in Roderick (1972) 488: When a man drops mateship altogether and takes to ‘hatting’ in the Bush, it’s a step towards a convenient tree and a couple of saddle-straps buckled together.
1936		(con. 1830s–60s) ‘Miles Franklin’ All That Swagger 352: They could combine the freedom of hatting with adjacence to a home and did not make off as formerly from any community where women appeared.