This is not an "operational" matter it is a "certification" matter covered under the Chicago Convention & other treaties and administered by ICAO. In "certification" matters the aircraft operates under the rules of the country of registration. An FAA AD or other ruling does not automatically apply to aircraft NOT registered in the USA. Fortunately international civil aviation operates under a VERY cooperative system under pinned by the convention. I really do not think there is a major problem.
Specifically applying this to QFs B744, purely as an example, my speculation, subject to more information becoming available, is that QF B744s do not have this modification, that QF will/has applied to Australia's airworthiness authority, CASA for a concession to operate the aircraft without it until its announced retirement in 2020, CASA would most likely grant it and the FAA will accept it. That's how the system works. I stress that the series of events described in this paragraph is pure speculation, but it is consistent with how the system works.
If a USA (FAA) issued AD has an action by date of 31 December 2019, irrespective of CASA decisions to the contrary, come THE date, QF's ability to operate the aircraft commercially to/from the USA will be impaired. If it does operate to the USA, there will be one off insurance cover written for each non-compliant aircraft operating to the USA.
Application of airworthiness rules ultimately stems from the United Nations, and operate in a similar way for surface vessels and aircraft. If you ply your flag of convenience vessel between two countries with low safety standards, and in transit, stay in international waters, not a problem. But if you venture into a port or waters of a country with higher standards, the vessel will be detained until brought up to local standards.
Commercial aircraft insurers (and maritime too, though not with the FAA, etc) incentivise operators / owners to meet / exceed airworthiness rules equivalent to, or higher than required by the FAA, EASA and in the case of QF, CASA.
Think of the issues that could arise if leasing or financing aircraft to countries with very liberal or no rules.