[A humble request: If you can, please donate to help me carry on tracing word histories. Thank you.]

 

Originally and chiefly British English, the colloquial phrase to throw one’s toys out of the pram, and its variants, mean: to behave childishly and petulantly, to throw a tantrum.
—Australian-English synonym: to spit the dummy.

The phrase to throw one’s toys out of the pram is  based on the image of a baby throwing its toys out of its pram in a tantrum. This was mentioned, for example, in the following from an account of a match between Chelsea Football Club, Fulham, London, and Burnley Football Club, Burnley, Lancashire, played at Stamford Bridge, Fulham, London—account published in The Kensington News & West London Times (London, England) of Friday 30^th January 1970 [page 7, column 1]:

[In] those last few minutes […] Chelsea threw away everything for which they had worked so hard—just like a baby throws all it’s [sic] toys out of it’s [sic] pram and then finds that there is no mother to pick them up.

These are, in chronological order, the earliest occurrences of the phrase to throw one’s toys out of the pram and variants that I have found:
—Note: Surprisingly, I have found no occurrence of this phrase between 1947 and 1987:

1-: From the column Observer’s Commentary, by ‘Observer’, published in the Evening Sentinel (Stoke-on-Trent, Staffordshire, England) of Saturday 5^th August 1944 [page 3, column 3]:

Baby Hitler—
Elsie and Doris Waters *, in their own sphere, are incomparable broadcasters. Their wit has its origin in cerebral capacity and intelligent observation and deduction. This, surely, is unrivalled among modern witticisms:—
Hitler is getting wild; he is throwing his toys out of his pram.

* Elsie Waters (1893-1990) and her sister Doris Waters (1899-1978) were British comic actresses and singers who performed as a double act.

2-: From Lord, I Was Afraid (London: Collins, 1947), by the British author Nigel Balchin (1908-1970) [1939-1945, chapter 6: An air raid shelter, page 180]—here, Jerry designates the German army:

There is a violent explosion, followed immediately by another that rocks the shelter. […]
[…]
Enter the SHELTER MARSHAL.
SHELTER MARSHAL All right in here? Nelson confides that every man. Bit rough but it won’t last. The steady British infantry. Jerry’s throwing his toys out of the pram. Hard pounding gentlemen. We shall see who pounds longest.

3-: From Gatting on a sticky wicket, by Fred Plester, published in Bedfordshire on Sunday (Bedford, Bedfordshire, England) of Sunday 13^th December 1987 [page 13, column 1]:

One of the few pleasures left to an Englishman is to get up early of a morning, whack on both bars of the fire before tuning into cricket played in some foreign land against a background of Imams calling the faithful to prayer.
At the time of writing hopes that the second test against Pakistan will continue look slim and even the tour itself is threatened.
[…]
It is of course the television playbacks which have given the English supporters the ammunition to sulk and the team to throw all its toys out of the cot. These playbacks have shown Mssrs [sic] Shakeel Khan and Shakoor Rana as not the type of chaps you would want to follow into the witness box or even administer a small trust fund for the family gerbil. They are, in short, conniving cheats whose saving grace is a refusal to accept bribes before stumps are drawn.
That is not the point. For the purposes of this farcical series they are the umpires and their word is law.

4-: From High aspirations, grandiose plans, about Bedford Rugby Club, published in Bedfordshire on Sunday (Bedford, Bedfordshire, England) of Sunday 20^th March 1988 [page 12, column 4]:

Much credit must go to Messrs. Chadwick and Cooley. They have coached fun and flair to somewhat inexperienced threequarters whose best asset is youth. The club went some way to shooting itself in the foot over Chadwick when they approached England B coach Alan Davies behind his back. A lesser man might have thrown his toys out of the cot. If Chadwick was miffed it did not show.

5-: From a letter to the Editor, by one Ray Ross, published in the Ripon Gazette & Boroughbridge Herald (Ripon, Yorkshire, England) of Friday 3^rd November 1989 [page 10, column 8]:

Political ping pong

Sir, When are we going to see our Ripon City Council working together in harmony to the benefit of the Ripon electorate? How long do we have to wait before our councillors realise that party politics have no part to play in local government?
[…]
[…] May I ask the City Council to call a halt to the ineffective style of “us and them” local government. Stop throwing your toys out of the cot. Put away your coloured rosettes while in committee and in military terms “fall back and regroup” then go forward as a team to fulfil the aims of the Ripon people.

6-: From Committee chaos, by Steve Hook, published in the Harefield Gazette (Hillingdon, London, England) of Wednesday 6^th December 1989 [page 4, column 4]:

Hillingdon Council is lurching towards a constitutional crisis. The Conservative Group, led by Cllr Andrew Boff, has brought things to a head by refusing to chair committee meetings. […]
[…]
Liberal Democrat group leader Cllr Tony Little said: “At first the Tories were just sulking, but now it seems they have finally decided to throw all their toys out of the pram. It’s all very childish.”