To set the scene:
In the (1917 Australian federal) election campaign (Prime Minister Billy) Hughes had promised not to reopen the conscription issue unless 'the tide of battle which flows strongly for the Allies turns against them'. In November 1917 this seemed to have happened and Hughes, under strong pressure, announced another referendum for 20 December. This time passions rose even higher, inflamed by mounting hysteria in Hughes and by the cold, Irish logic of
Archbishop Daniel Mannix. There was a degree of violence unusual in Australian politics, which turned to farce when Hughes, after being struck by an egg on the railway station at Warwick, Queensland, promptly established a Commonwealth police force to combat disloyalty. The referendum was lost by a larger majority than before. Hughes had unwisely declared that he would not govern without conscription. He accordingly resigned, but the governor-general, unable to find anyone else who could command a majority, recommissioned him with the same cabinet as before.
Source:
http://adb.anu.edu.au/biography/hughes-william-morris-billy-6761
Now, let's suppose that instead of an egg, a brick is hurled by the demonstrators at that Warwick train station towards the Prime Minister. What was IOTL a slightly farcical scene instead results in the death of Billy Hughes in the midst of an extremely divisive referendum on conscription.
The number of short-, medium- and long-term butterflies that could result from this are fascinating.
How do the people of Australia react in the short term? Hughes was a polarising figure, nevermoreso than at this point of history. Are there violent demonstrations after his passing?
As the visible face of opposition to the referendum, although entirely unconnected to the Warwick Incident, what is the fate of Archbishop Daniel Mannix? What about Queensland premier T.J. Ryan, who was a staunch opponent of Hughes and of the conscription movement? He attempted to move into federal politics and was thought of as a potential future leader of the Labor Party before his untimely death in 1921 - with the assassination of the PM in his home state, does Ryan become a pariah?
With Hughes now a martyr for this cause, does the referendum on conscription succeed? In Australia, referendums are very hard to pass: there must be a majority of votes overall as well as a majority of states (4 out of 6) approving any change. IOTL the referendum received 46% support and passed in only two states. It very nearly passed in Victoria though (less than 3000 votes, or 0.5%, difference).
In the short term, who succeeds Hughes?
Here is his cabinet as of November 1917. I see three likely candidates: Cook, Forrest and Watt. Cook had already been Prime Minister prior to World War I and was Hughes' unofficial deputy. The 70-year old Forrest may feel he had more of an entitlement to the job, but he is already dying of cancer (and did so in 1918. Watt had not been in federal parliament long, but was a former Premier of Victoria and would be Acting Prime Minister IOTL when Hughes went to the Versailles Peace Conference.
It is worth noting that at this point in Australian history, no Prime Minister had passed away in office, so no precedent exists for the Governor-General to appoint a successor. (Future precedents would see the Deputy Prime Minister (Forde) or leader of the junior Coalition Party (Page, McEwen) be given the role in a vacancy)
Who becomes the next Prime Minister may simply be a case of who can get to the Governor-General first.
Looking big-picture, what happens to the non-Labor side of politics? Is the Country Party butterflied away? What happens to the career of Stanley Melbourne Bruce without his early mentor? Do the Nationalists stick together and survive beyond the Great Depression, or do they splinter apart before even then?