I'm not seeing anything unusual in those charts, other than maybe the warm fronts?

IIn Perth I feel like the rainy months are arriving about a month late and hanging around a month later. Also the winter rain seems to come from the North more often.

High pressure systems drifting from west to east over Australia over the cooler months is normal except in the wetter years. This weather is characterised by settled weather of cool nights, warmer sunny days and no rain.

Cold fronts hit the high pressure systems and are pushed to the south.

That thing is a not a cold front. It is a kind of like a mixed or stationary front.

Tail of the Cracken