ALL International Civil Aviation (ICA) is conducted under the rules established by the Chicago Convention of 1944 (the Convention).
The rules today for all aspects of ICA including airworthiness, flight crew/ATC licencing, operational procedures, etc are issued by ICAO (International Civil Aviation Organisation) established by the convention.( But not including traffic/route rights, which are NOT covered b the convention). ICAO is a standards setting body and each country that signs the convention becomes a member. It is based in Montreal, Canada and is a UN administrative body.
The day to day operations of ICA are under the control of the national aviation bodies. In Australia this is the Civil Aviation Safety Authority (CASA), in Europe it is European Aviation Safety Authority (EASA) (replaced JAA), in the USA its the Federal Aviation Authority (FAA) and so in each country. Some small countries may contract out their national authorities to other countries, so Australia's CASA is also the PapuaNew Guinea authority and New Zealand's authority is the national authority for the Cook Islands. There are undoubtedly other examples.
The FAA and EASA are only "policeman" for their own jurisdictions. Where they are more prominent than other national authorities is that the convention places extra responsibilitys on the authorities of those countries which manufacture aircraft. And which are the authorities of the countries which manufacture most of the worlds aircraft? EASA and the FAA, of course.
But every airline that wants to operate an aircraft has to be sure it has a type certificate from its own national authority. So when QF
fronts up to CASA with applications for Certificate of Registration & Airworthiness for A380 MSN
14 it will have to, in effect, get an Australian type certificate for the A380, before it can operate it. This used to called a "first of type" certification and the first question is are you basing this application on the EASA or FAA requirements? And the second is, does the aircraft already have EASA or FAA type certification? If please attach a copy! CASA will then advise of an extra requirements it may have for Australian type certification.
Of course this process has in fact been underway ever since QF
first ordered the aircraft and any modifications required by CASA would have been designed and implemented into the production process from the beginning of construction.