About 20 years ago, although it seems like yesterday I spent 2 weeks in the Perth area with my bike during August (winter!). I took a mountain bike kitted out with slicks suitable for road and gravel tracks. Did day rides from Perth for the first week then did a linear tour down to Margaret River in week 2. Up in the 'mountains' I rode mostly on gravel tracks. Not sure I would entirely recommend this as days spent on deserted forest racks on washboard surfaces can get a bit gruelling! The main roads out of town were scary as the lorries there are enormous and don't give any space for bikes.
To make the most of my time, I called into the office of Bicycling Western Australia on my first day, had a good chat with the staff there and picked up a bunch of maps. These formed a good basis for getting to know the area and get the most from the time. In case you haven't found this really good resource yet here is the link.
https://www.bwa.org.au/bikes-and-riding/231/. I was staying in Perth with expats working there so also got lots of tips about places to visit which I then rode to. The cycling infrastructure there in the 90s was still leagues ahead of the setup back here in GB.
There aren't really any high mountains to give challenges which I had hoped for, but the wildlife, nature and coast more than made up for this. Amazing.
Enjoy your time exploring!
