Vendors typically ship parcel post to Western Australia as a standard practice but since the parcel will only contain BAC water and nothing prohibited, express post might be an option if you discuss this with the vendor beforehand.
If you need it as quickly as possible and can not source it locally or a vendor willing to post it out to you express, take a look at Glass Vials Australia. They also offer delivery via courier (at an additional cost) which would get it to you faster than AusPost express too:
https://www.glassvials.com.au/solvents-carriers/103-bacteriostatic-water-20ml.html
AJ