Extract from OED Online

short, a., n. and adv.

SECOND EDITION 1989

DRAFT ADDITIONS JUNE 2005

colloq. (orig. Austral. and N.Z.). Usu. depreciative. short of a and variants: lacking in common sense or intelligence, mentally deficient, slightly crazy; generally expressed in terms of some (specified) deficiency in a desirable or standard quantity of something, as a brick short of a load, a few sandwiches short of a picnic, sixpence short of a shilling, etc. See also a shingle short s.v. SHINGLE n.¹ 1b, and cf. to have a tile loose s.v. TILE n.¹ 1g, not all there s.v. THERE adv. 12b.
Variants of these phrases also occur in the form lacking (also missing, wanting) a shingle (brick, etc.), not the full shilling (quid, etc.), and similar.

[1852 G. C. MUNDY Our Antipodes iii. 17 The climate is productive..of chronic diseases rather than acute ones. Let no man having, in colonial phrase, ‘a shingle short’ try this country. He will pass his days in Tarban Creek Asylum.] 1885 R. C. PRAED Austral. Life 199 He had always understood that Rachel Murray was short of a sheet of a bark

the Australian equivalent of ‘a tile loose’. 1939 P. A. EADDY 'Neath Swaying Spars 117 The old captain..must have been what some people term ‘a hapenny short of a shilling’. 1960 N. HILLIARD Maori Girl II. vi. 213 Not that she was simple in the sense that she was short of the full quid. 1983 R. THOMAS Missionary Stew xv. 133 Velveeta's sort of pretty and halfway smart, even if she is six bricks short of a load. 1992 Making Music May 19 If someone's obviously several bananas short of a milkshake, how you deal with it depends on whether they're the star of the show.

1993 R. LOWE & W. SHAW Travellers 28, I thought either I had something very wrong with me physically, or I was two sandwiches short of a picnic.

1996 Independent 26 Mar. 13/1 The following suggestion..comes from a leader of Conservative-controlled Westminster Council, so he will want to treat the proposal with respect, even though it is one spark plug short of an engine. 1999 M. SYAL Life isn't all Ha Ha Hee Hee ii. 70 At first, her child-like playfulness had worried him, alert as he was to the local whispers of the girl being a few chapattis short of a thali.