The Australian Quarantine Service AQIS is the only definitive source for a ruling on what is required. The words they use for having a vehicle inspected is that they expect it "to be as clean as a new vehicle". With any untreated wood they will looking hard at it - seeing as how most plywoods are treated with various glues then I dont think it will attract too much extra attention.
I'd be more worried about mud, seeds, plant waste etc. up behind panels that you never new even existed - but AQIS officers are aware of. Get a copy of the AQIS inspection standards, whats allowed, whats prohibited, what MUST be declared and make sure that you comply. If in doubt ask them before shipping, its cheaper to fix a small problem when you have control of the vehicle, once AQIS have it the costs can escalate very rapidly.
The RoRo vehicle ships which unload at specialist wharves are setup to deal with vehicles - they have cleaning facilities, waste disposal, etc. Having a vehicle broght in by container can mean that when AQIS inspect (if it fails) it has to be taken back to the "vehicle" wharf in the container for cleaning.