Each state in Australia has different licencing laws, so you need to check with WA driver licencing authority, but quoting from the RTA, New South Wales it seems the recognition is the same across Australia. It seems your UK car drivers licence will be accepted, but your Taiwan motorcycle licence will not be accepted:-
Recognition of licences from certain countries
The recognition of licences from certain countries was agreed nationally and commenced in NSW on 20 May 2002.
When
converting your overseas licence to a NSW licence, if you hold an
acceptable driver or rider licence from one of the recognised countries
below, you will be exempt from:
Note: The exemptions only apply to applicants for Class C (car) and Class R (rider) licences.
Recognised countries
Austria, Belgium, Canada, Croatia, Denmark,
Finland, France, Germany, Greece, Guernsey,
Ireland, Isle of Man (licences issued since 1 April 1991), Italy, Japan, Jersey, Luxembourg,
Malta
(licences issued since 2 January 2004), Netherlands, New Zealand
(except where a paper licence is presented), Norway, Portugal,
Singapore, Spain, Sweden, Switzerland, United Kingdom, USA.