A JP appointment in Queensland has powers relating to Statutory Declarations in Queensland and the Commonwealth. Statutory Declarations made under other States and Territories' jurisdictions may be able to be witnessed in Queensland by a Queensland JP. It is up to the authority as to whether they would be acceptable. Make the client aware of this before witnessing the document.
Use the same process outlined in Statutory Declarations, and you must note beside your signature that you are a JP (Qual) "for and in the State of Queensland".
The New South Wales Oaths Act 1900 recognises the authority of JPs in other States to witness a NSW Statutory Declaration made in that State. Note the identity requirements for the jurat as in Identity Verification.
JP Handbook Chapter 4.12
QJA Journal Volume 13 Number 1 Autumn 2016
Technical Bulletin 06/12