Spring (Sept-Nov) and Autumn (Mar-May) are ideal times in which to visit Perth. Spring is perhaps the very best to see the sights as after a decent winter's rainfall, the famous wildflowers around Kings Park and the Avon Valley bloom splendidly. Beach-goers from colder climes might find the summer months too harsh, so it is perhaps best to visit during March-April or October-November.
Although Western Australia has many public holidays they are unlikely to cause much inconvenience to your travels. Shops are still open, public transport still runs and the sky is still blue. The exception may be New Years' Day (Jan 1), Australia Day (26 Jan), Good Friday (Apr 2), Easter Monday (Apr 5), Labour Day (first Monday of March), Queen's Birthday (Sep 27) and Foundation Day (first Monday in June) and Christmas Day (Dec 25). Most larger shops and shopping centers, pubs and restaurants are closed on these days but smaller convenience stores and some fast food chains keep their doors open. This said only some shops open, most shopping centres and large stores will close for public holidays and Sundays.