I use my girls WA one in QLD plenty of times.
Can I use my NSW-issued permit elsewhere in Australia?
Yes. All States and Territories in Australia are participating in the Australian Disability Parking Scheme. However, as the concessions may vary between each State and Territory, you should contact the relevant authority for complete details.
In all cases, a visiting permit holder must comply with the disability parking concessions applicable in the State or Territory they are visiting.
The Commonwealth Government's Australian Disability Parking Scheme website provides links to all State and Territory information on disability parking schemes across Australia.