A surviving Obrenovic Serbia is quite unlikely, although a pro-Austrian Serbia would have interesting effects on the Balkan alliances. Austrophiles in Serbia were rare and unpopular given that Serbian interests either laid in Ottoman Empire or Austria-Hungary.
There will be another assassination attempt, and even if that fails and Obrenovic dies without heir, there might a be diplomatic crisis after the successor is unknown. Montenegrin claim to the throne might receive some backing from the great powers as a stabilizing solution, although a local noble might simply be 'found.' Serbia and Montenegro still get territory from the wars against Ottoman Empire, although the pattern of alliances that led to disastrous Second Balkan War might be changed.
Serbia joining the Central Powers would be quite unpopular and would have to require concessions at the expense of Austria-Hungary.
Yet another question: with a relatively pro-Austrian Serbia (or at least non-committal during the opening stages of the *First World War) would the A-H Croats even want to be part of a Yugoslavian state after the collapse of the Empire? Could we see an independent Croat-Slovene-Bosniak Republic a la Czechoslovakia?
A Bosniak Republic is not likely to exist, given that Bosniaks are not considered a people then. There was a Slovene-Croat-Serb state that existed as interim entity for a month before the Kingdom of SCS was established.
Given that Croatian national movement spawned the idea of Yugoslavism and Serbia is idolized as a possible Piemonte/Prussia of South Slavs in literature, the answer is a resounding yes. Every political option will argue for a joint state with other South Slavic peoples. All other political alternatives are a triarchy South Slavic state under the Habsburgs or the fantasy for a Croat dominated independent South Slavic state backed by Russia (entirely unrealistic ideas).
Peasants emerging as a independent political force happened only in the aftermath of the Great War and after great effort of Radic brothers to politically mobilize them - it was a complete surprise to everyone, even after the Green Cadre scare (everyone believed peasants will return to inertia).
A Southslavic state will be attempted in the aftermath of the Great War. Serbia will still be a technically victorious power, as it will either be the country that incites the war or joins it later on against Austria-Hungary.
If, by some unlikely miracle, Serbia is on the same side as Central Powers and loses, a southslavic state is still attempted, although this time it is more likely that Serbia and Montenegro are invited to join the State of Slovenes, Croats and Serbs since Serbia too will lose territory to Entente aligned balkan states.
Without Serbia being victorious, there is more room to negotiate the form of the future state unlike OTL and future state might end up a constitutional monarchy (if Serbian monarchy survives). A surviving State of SCS would be interesting although very implausible. For example, its quorum was only 33%, the president was a Slovenian, the seat of government was in Croatian Zagreb and so on... It has all the hallmarks of Weimar Republic idealistic inefficiency.
A bit more widespread in Dalmatia, but not much.
That doesn't sound quite right. Dalmatia is in fact the only region in A-H where Croatian nationalist and Yugoslav parties initially grew comparatively weaker, due to a strong local tradition of praising Dalmatian identity and Italian heritage. The Authonomashtvo movement opposed Dalmatia joining with Croatia and Slavonia (region in Croatia, not Slovenia), but was quashed after the Croatian nationalist party became the regime party. Census reports until the Great War show that regional identity movement stayed alive despite it being politically dead.
There will be still threats from anarchy (that Halagaz described) and someone will have to be invited to deal with the mess. The movement, although numerous on paper, is very disunited. Peasants are viewed as separate from ordinary urban citizens and vice versa. Now, they've been conscripted into a losing war in a conflict they barely understand and the state that did it fell apart. Its members are mostly the starving former conscripted soldiers looking to survive in state of uncertainty.
It would be impossible for them to coalesce even into a short lived peasant state without a previous leader (Radic brothers, OTL peasant leaders, would be tempted, but opposed to a peasant republic since they tried to politically educate and incorporate peasants into political life) so that would probably require an additional POD. There might be widespread riots, but I doubt they will unite or coordinate in order to establish their own Soviet or Peasant Republic. After they are put down, they will be forgotten by everyone except a select few (like Radic brothers).
Entente might leave it to Italy to put it down (with catastrophic consequences), but the new government likely invites help from neighbouring states, possibly evenly Czechoslovakia or Romania (avoiding countries with territorial aspirations), warning against a possibility of a third communist state, especially near the Magyar Soviet Republic.
The new Southslavic state ends up with concessions given to Italy and other countries, a compromise agrarian reform is attempted and eventually pushed through. In the new state, nationalists try to get support of the now politically relevant peasants, but so might the communists, a rivalry between Croatians and Serbians will reemerge, and things get fuzzy. The constitutions is likely a compromise that no one will like and there will be a strong impulse for a central authority. Perhaps even an quasifascist movement emerges, mimicking Italy and Germany and promising to restore the glory of 'Illyria.'
Although Serbian hegemony was quite problematic for first Yugoslavia, it overshadowed many other problems managing to eventually band disparate factions together. The new state will suffer from corruption, unpopular and opportunistic politicians and so on. I foresee that the main struggle in interwar Yugoslav state will be between a a possible national unity irredentist front and national agrarian-populist front. Of course, Croats and Serbs might simply just clash again but scales being a bit more balanced (Serbs will still be in advantage though). Croats becoming the main force behind agrarianism and Serbs behind irredentism.
