WA only got Sunday Trading allowed last October I imagine it'll be sometime before anywhere but the Servo/Marts are 24hrs (but there are a couple of those)
The IGA's are open till about 9 or 10pm I think (nearest ones are Merriwa or Kinross) and also Basil's in Mindarie is open till about the same time. The petrol stations might be open a bit later but that's all.
I'm not aware of any 24 hour supermarkets in the whole of Perth!!