Ok, here is a .pdf on disability parking for Australia, by state. ACROD is the oversight for Australia on disabled parking. Each State have their own unique rules and regulations to disabled parking. Some allow for mental illness, some not. I dare say, each application is taken on its own merit, and with physician advice in hand.

The WA application and guidelines are here.

That should help you to enquire. I know that Queensland allow a red parking permit for the exact thing as you encountered, for mental illness disabilities, though not every state does this. You need to read the ACROD site, linked above, which outlines each state in detail with links to all forms and contacts.

Hope that helps!