Green’s Dictionary of Slang

1. (Aus./US) a fool, an eccentric, thus attrib. [SE wombat, a burrowing marsupial resembling a small bear].

1908		Bulletin (Sydney) 24 Sept. 14/2: [L]o and behold! the map is upside down to you, and when he scratches a line straight in the direction of your right big toe and tells you to go that way, from your point of view you should go the opposite. [...] And it never strikes the old wombat from his point of view.
1922		S. Lewis Babbitt (1974) 156: Come on, you wombats!
1936		(con. 1830s–60s) ‘Miles Franklin’ All That Swagger 361: I’m only an old wombat.
1979		(con. 1962) G. Wolff Duke of Deception (1990) 209: Club members [...] gave a grade to the sophomore, from the highest (1: ‘ace’) to the lowest (7: [...] ‘lunchmeat,’ ‘banana,’ ‘wonk,’ ‘wombat,’ ‘turkey’).
1985		R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 88: Listen, you team of wombats [...] All I want is a bit of sleep in the morning.
1986		R.G. Barrett Godson 23: ‘This wombat grandson of mine’.
1990		Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Wombat. A ponderous person.
1992		R.G. Barrett Davo’s Little Something 25: Only having to put up with you and the rest of these wombats.
2006		B. Matthews Intractable [ebook] ‘Fucking wombats!’ he was screaming. ‘Can’t get a fucking clean pinch so they load a man up’.

2. (US campus) an ugly person.

1985

Eble Campus Sl. Oct.

3. a pointless occupation, i.e. waste of money, brains and time.

2000

Daily Tel. 10 Jan. 19: I’m particularly pleased by Wombat, which is short for ‘waste of money, brains and time.’.