Apparently of Australian-English origin, the phrase all duck or no dinner means all or nothing—Australian-English synonym: Sydney or the bush.
The image is of a dinner composed entirely of duck, i.e. of choice food, as opposed to no dinner at all.
These are the earliest occurrences of all duck or no dinner that I have found, in chronological order:
1-: From the Cricket section of the Prahran Chronicle (Prahran, Victoria) of Saturday 7th December 1895:
The match of the season next round—South Yarra v. St. Andrew’s.
Yarra say St. Andrew’s will get a taste of their batting powers.
“All duck or no dinner” is the Yarra’s motto for the next match.
2-: From Mining News, published in The Coolgardie Miner (Coolgardie, Western Australia) of Thursday 17th February 1898:
The holders were offered £200 for a fourth interest in the claim, but they refused, stating that it was to be ‘all duck or no dinner’ with them. A few days afterwards, £800 was offered to them for the same interest, but this large offer was also refused. They bottomed in due course, and obtained about 250oz of free gold on doing so.
3-: From an article about “the difficult question of providing the people [of Tasmania) with means of communication”, published in The Circular Head Chronicle (Stanley, Tasmania) of Wednesday 29th August 1906:
Surely it is time the Government evolved some scheme to enable the settler to remain on the land. If railway construction is too costly let us have tramways or roads. When private enterprise proposes to build 25 miles of tram line for £4000, the estimate of £7,500 a mile for constructing a railway seems somewhat prodigious. And yet no middle course appears to suggest itself to the Government. The people are not clamouring for “all duck or no dinner.” The average out-back selector would be well satisfied with a line costing one quarter of the Government’s estimate. In fact any scheme would be acceptable if it afforded the relief required.
4-: From the horse-racing section of The Cootamundra Herald (Cootamundra, New South Wales) of Saturday 1st February 1908:
Seldom Fed ran 2 miles in 3.52. He gallops very high, and I think all that is wrong with him is that he is not judiciously placed. If his nominators would abandon the “all duck or no dinner” idea, and place him in Trial Stakes and Hack Races, it would be more profitable.
BRITISH- AND IRISH-ENGLISH OCCURRENCES
These are the earliest occurrences of the phrase that I have found in British and Irish English:
1-: From Alan Fairfax on the Cricket, published in The People (London, England) of Sunday 27th August 1950:
In this needle match * at the Oval between Surrey and Lancashire, it must be all duck or no dinner for Surrey. They have a game in hand and need 16 points to share the championship, or 24 to win it.
(* The colloquial British-English phrase needle match, or needle game, denotes a sporting contest attracting much interest and excitement, or arousing exceptional personal antagonism between the contestants.)
2-: From a letter to the Editor, written by John Cowser, President of the British Music Society, published in the Belfast News-Letter (Belfast, County Antrim, Northern Ireland) of Saturday 30th June 1951:
Sir—May I, as President of the British Music Society, add an explanation to the letter Mr. Sidney Griller was good enough to write to you on the cancellation of the Octet concert. […]
[…] The expense of bringing to Belfast eight leading artists is considerable; we felt this difficult to justify if they were to combine for the shorter of the two works only. It was a case of all duck or no dinner. A suggestion to postpone the concert to September was blocked by the fact that the Grillers leave for America at the end of August. Alas, no dinner it is.
3-: From Contract Bridge, by ‘Duplicate’, published in the Belfast News-Letter (Belfast, County Antrim, Northern Ireland) of Saturday 16th January 1954:
At Table 4, South opened One Club after a pass from East, and West bid One Heart. North, rather stuck for a bid, diffidently doubled, and was rather relieved when East went out into Two Diamonds. South thought it would be a waste of energy to double that, and deciding to trust his partner for a semi-guard in Spades, bid Three No Trumps. West doubled violently, and the bid came round to South, who redoubled. All duck or no dinner.