My guess on this is that we’ll have an election sometime between now and end of October.
Turnbull must know he’s a dead man walking. He could easily call an election today or tomorrow and go out with all guns blazing. This would deny any would be challenger of the Prime Ministership.
If he doesn’t do that, Dutton or however becomes leader will have to go to the Governor General and convince him that they are capable of forming a government. If Turnbull and/or a few others state that they won’t guarantee supply, the GG would be in his right to dismiss the government and call a general election.
This won’t be good for the LNP.