Why do Australians and NZers call snacks/lunch *crib*?

Solution 1:

Ok I just looked it up in the OED, which is what I should have done yesterday. The first recorded usage of crib to mean "food" or "a light meal" predates James Cook, i.e. the first European contact with Australia.

dialect, Australian, and New Zealand. Food, provisions; a light meal or snack; a piece of bread, cake, etc. Frequently attributive.

• 1652 R. Brome Joviall Crew ii. sig. F3 Here's Pannum and Lap, and good Poplars of Yarrum, To fill up the Crib, and to comfort the Quarron.
• 1825 J. Jamieson Etymol. Dict. Sc. Lang. Suppl. (at cited word) Haste ye, and gi'e me ma..crib, Guid-wife.
• 1872 Notes & Queries 4th Ser. 9 47/1 The gift..was generally a small cake..and was called the ‘christening crib’—a crib of bread or cake being a provincialism for a bit of bread, &c.
• 1880 M. A. Courtney W. Cornwall Words in M. A. Courtney & T. Q. Couch Gloss. Words Cornwall 15/2 Crib, a crust of bread; fragments of meat. ‘Eat up your cribs.’
• 1881 Trans. Amer. Inst. Mining Engineers 1880–1 9 124 Crib...3. A miner's luncheon.
• 1889 Daily News 4 Apr. 4/8 In the pocket of each of the garments was a pasty and a ‘crib’ (apparently a small loaf).
• 1904 ‘G. B. Lancaster’ Sons o' Men 159 Sereld..growled because someone had spilt tobacco-ash into his crib—which is bushman for dinner.
• 1908 Westm. Gaz. 13 May 6/1 Half an hour's ‘crib’ time [at Blackball, N.Z.] is also granted.
• 1926 K. S. Prichard Working Bullocks xi. 108 Red picked up his crib-bag.
• 1928 J. Devanny Dawn Beloved xxx. 273 He stopped..to hang up his towel and crib tin.
• 1942 A. L. Rowse Cornish Childhood ii. 30 He used to take it to work with him and at crib-time (i.e. lunch-time) would entertain his fellows with it.
• 1947 A. Vogt in D. M. Davin N.Z. Short Stories (1953) 364 Ben went to work [in the bush] each day like the rest of the men, with his crib and oil-skin.
• 1954 Coast to Coast 1953–4 37 Jacques was holding out his crib. ‘Time to eat.’.. Crib over, the men rolled cigarettes.
• 1971 J. Turner Stone Dormitory iii. 30 ‘Just come in for me crib. It's time.’.. ‘It's ready for you, Tom,’ she said, putting the bread and cheese and tea before him.

Based off of this I am not so sure about Cornish though. Richard Brome was English who as far as I can find spent his adult life in London, and John Jameson was Scottish.

Solution 2:

Probably, as suggested by GDoS, from the following sense of crib:

crib n.2

(SE crib, a container for animal fodder)

3. (Aus./N.Z.) a snack, a light meal, a piece of bread, cake etc; thus crib bag, crib break, crib room, cribtime.

   • 1870 [UK] Old Hunks in Darkey Drama 5 53: harry: I’m witness that you promised to give Tommy something better than a crib. tommy: A good round dinner.

   • 1900–10 [Aus] Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 52: CRIB: miners term for a twenty-minute interval for food or smoke-ho, known as crib-time; and lunch carried to work is known as crib.

The Cornish origin seems plausible. From List of Cornish dialect words:

Crib - a mid-morning break for a snack.

The Oxford English Dictionary (2nd ed.) has "Food, provisions, light meal, etc." (dialectal) as one of the meanings of "crib" giving several examples including quotations from M. A. Courtney's Glossary (1880) and Rowse's Cornish Childhood (1942).