The probable location is outside Australian territorial waters (12 mile limit) regardless of whose FIR or SAR region it is in. Therefore under ICAO rules this now falls to the State of Registration (Malaysia) to conduct the investigation the ATSB is NOT the lead agency and has no right of participation.
Annex 13 Section 5.3 is the standard:
5.3 When the location of the accident or the serious incident cannot definitely be established as being in the territory of any State, the State of Registry shall institute and conduct any necessary investigation of the accident or serious incident. However, it may delegate the whole or any part of the investigation to another State by mutual arrangement and consent.
Only 2 other States have rights of participation, the USA (Design / Manufacture of the airframe) and the UK (design / manufacture of the engines)
That said Malaysia can call on Australian assistance and probably will in relation to wreckage search and recovery.
5.3.1 States nearest the scene of an accident in international waters shall provide such assistance as they are able and shall, likewise, respond to requests by the State of Registry.