Unless you are doing a long distance hike, or just hanging out on a beach somewhere, a car or an arranged tour is required to see all the highlights of the region. Bicycle touring, especially around the Margaret River region, is popular, but as always requires some preparation and route planning - the roads in the area often have no shoulder and have fast traffic.
A map can give you little indication of driving times, and even GPS and online mapping services can grossly misrepresent these times. Seek local advice.