From what I’ve found from personal research, Disability Certificates/IDs are typically not recognized beyond the local area or nation they are provided by.
In the United States if all you’re looking for is a Disability Parking pass, those are issued to residents of a state and requires proof of disability & residency. So, unless you own property, I don’t believe you can even start to get one as a foreigner (however, this may vary by state). The US does recognize other countries’ parking permits to a certain extent (depending on origin country & individual US state laws), but as you found out you must have one already. It may be possible to rent a Wheelchair Accessible van (I don’t know availability in Australia), but I can’t say if it will already have Disabled Parking plates.
For services beyond parking permits, sadly none of my disability paperwork is valid in most countries outside the US where it cannot be checked easily in that country.
I have heard of that Disability Card website, and for use in any official capacity I can say it will NOT be beneficial in most cases. Two reasons for this being that you can just make up a fictional disability and buy this ID, and second is the disclaimer the Disability Card company has stated on its website, quote:
Disclaimer
Please note that our card obviously is not a government issue card and cannot be replaced by such in any country. You cannot open with our card for example a bank account or it cannot replace a driving license or a Passport.
Essentially the ID card they provide is no better than a printed-out list of your disabilities. Which instead of buying this card I would recommend doing along with listing any accessible needs you have (and if necessary, translate it into whatever local countries language you are traveling to), but I don’t know if it will help with your situation.
As for another reason to avoid such websites, the site you mentioned supposedly give you a disabled parking permit pass for a car with a 5-year paid subscription. Except from the tiny picture they show of it, and the fact that you’re buying it with no proof of disability, I have to assume it’s not a legal permit (my guess is that the unreadable fine print on it states as much). If so, then it could potentially cost you even more if you are caught using it or worse (e.g., while they may just let you go as a tourist, in Florida using an illegal Disability Permit could cost you a fine of US$500 and up to 6-months of jail time).
I hope someday soon we get a real internationally recognized Disability ID in the US and other countries, to make stuff like this easier to manage.
Sorry I couldn’t help more with your situation.
-Justin