I don't think you will need a skills assessment if you're going on your OHs 136, - the skills assessment gives you a code which you then put onto your application.
However, if you want to register to work as a nurse, each state has their own nursing board and registration isn't held centrally like in the UK. The nursing board of WA wanted similar things i.e certified copies of certificates, etc., as the ANMC who just pass the file on.
The website is:
www.nbwa.org.au