Green’s Dictionary of Slang

dunny n.2

also dunnee
[dunnaken n.]
[1930s+] (Aus./N.Z.)

1. any lavatory; also attrib.; thus dunny cart, a vehicle used to remove excrement; dunny man, a night-soil cleaner; dunny roll, lavatory paper.

2. an outside lavatory or privy; also attrib.

In compounds

dunny-brush (n.)

[1980s+] (Aus.) a term of abuse.

dunny budgie (n.) [facet. use of budgie n.2 ; i.e. the size or noisiness of the flies is reminiscent of the bird]

[1990s+] (Aus.) a fly.

dunnygasper (n.)

[1960s+] a latrine cleaner.

dunny rat (n.)

[1980s+] (Aus./N.Z.) a cunning person.

In phrases

down the dunny

[2000s] (N.Z.) failed, disastrous .

flap like a dunny door in a high wind (v.)

[2000s] (N.Z.) to act in a panicky, nervous manner.