I know with the US that is to do with the 9/11 incidents regarding the O2.
Emirates, normally make the patient see a doctor beforehand to ensure that they are fit to fly, and if the passenger needs oxygen for whatever reason it must be stated on the form. Sometimes, the airline will make them see an Aviation Doctor beforehand as well, normally oxygen has to be pre-ordered before flying and can be on a constant flow/on demand out of Oz they will have to put on extra oxygen which I dont know whether there is a charge as some of the areas in Oz there arent hospital facilities within so many miles of the plane flying - eg bush areas. Best thing you could do is contact the Emirates office directly and they will advice the best thing for the patient.