I'm from over that way. Lots of climbing if you're prepared to drive a bit. At that time of year you want to be south of Perth, which really only rules out Kalbarri.
In and around Perth itself there are a few quarries which a mix of sport and trad. Mountain Quarry is probably the pick of the bunch and only around 40 minutes from the city. The rock quality at all the quarries is a bit suss and you'll want to get there early or late to avoid the heat. People bitch and moan about the quarries but actually, if you're stuck in Perth, they provide pretty reasonable and convenient climbing.
South of Perth you've got a couple of different options in the Margaret River area. Wilyabrup for sport and trad on granite in amazing ocean side location with easy access. There are a few pics in Simon Carter's recent book. This is a must do based on the location if nothing else.
Then you've got Bobs Hollow also in Margs. Bobs is lots of quite steep limestone, all bolts. Bit more of a walk in although it's very picturesque as you walk along the Cape to Cape trail. There's also a bit of bouldering being developed around the Margs area but I haven't done any of it. Obviously you also have access to world class surf and great food and wine, making Margs a pretty good all-round performer.
Further South there is cool sea cliff climbing at spots like West Cape Howe and The Gap (Albany). A 4WD is handy for some of these spots, especially WCH. Mix of sport and trad but you'd definitely be missing out if you didn't have a rack. Much of the climbing here involves rapping in.
There are other spots in the Porongurups (Castle Rock is supposed to be good) and Stirling Ranges, but I haven't been to those.
If you haven't got one try and pick up a copy of West Australian Rock. It's probably the best guide book, albeit a bit out of date now. Also worth posting on the WA equivalent of Chocky http://www.climberswa.asn.au/forum/