There are plenty of rivers in Western Australia that are suitable for overnight trip. Here are a few to get you started:
Murchison River: the journey from Murchison House station to Kalbarri is a wonderful two-day paddle with fantastic camping sites on the northern side of the river. Contact Murchison House station to arrange camping access.
Murray River: the upper and middle sections of the Murray River near Dwellingup have great sections of river and excellent campsites. Pinjarra to Mandurah is a great overnight paddle with camping available at the Ravenswood Caravan Park.
Blackwood River: the Blackwood is probably the premier canoe camping river in the State with a range of sections available. The areas around Sues Bridge, Warner Glen and Alexander Bridge all provide great opportunities.