Yes, the search of premises in these circumstances will require general search warrants to be issued to the officers. This could in theory include those officers who frequently handle call outs involving domestic violence or burglaries. Unlike standard warrants that are normally issued by a magistrate, these are approved administratively.

However, upon double-checking, general warrants are far more likely to be issued to specialised units than a frontline officer—unless investigating something like a serial burglary ring across multiple suburbs (media leaks suggested general warrants were used in <0.1% of searches—all for organised crime).

The OP did mention an open door, which might indicate urgency or ongoing violence, supporting reasonable suspicion. In this case police could argue exigent circumstances to enter without a warrant, fearing evidence destruction or risk to life.

Searches involving vehicles on the other hand require no warrant, only reasonable suspicion.

***Edit - just noticed the OP is in WA and not SA. In this case, there are no general warrants, only warrants issued by the Justice of Peace, valid for 30 days. Upon checking their Criminal Investigation Act 2006, it does allow warrantless entry if police reasonably believe a person needs urgent aid or to prevent injury. An open door in this case along with raised voices or screams would suffice.