I think any reading of the Australian Constitution clearly shows that our founding fathers did not foresee a situation where the Government of Australia would cede sovereignty to a foreign court. The Queen yes, it makes it clear the Queen is our head of State and has ultimate authority, but that is not what we are talking about here. Lets look at the relevant sections of the constitution:
Constitution of the Commonwealth of Australia
71. The judicial power of the Commonwealth shall be vested in a Federal Supreme Court, to be called the High Court of Australia, and in such other federal courts as the Parliament creates, and in such other courts as it invests with federal jurisdiction...which means it can invest jurisdiction in a Court, but the Waterside Workers case clearly stated the Court must be duly constituted (sometimes called a section 111 court). The Kangaroo Court in the ISDS would not be allowed.
72. The Justices of the High Court and of the other courts created by the Parliament--
(i.) Shall be appointed by the Governor-General in Council: and the Justices are appointed by the Governor General, not the Multinationals. Again this has been strongly defended by the High COurt in the Wheat and Waterside Workers cases.
A reference in this section to the appointment of a Justice of the High Court or of a court created by the Parliament shall be read as including a reference to the appointment of a person who holds office as a Justice of the High Court or of a court created by the Parliament to another office of Justice of the same court having a different status or designation. ie if it looks like a Court and smells like a Court - it is a Court and 72(i) applies - see the Waterside Workers case for a very strong defence of this section.
75. In all matters--
(i.) Arising under any treaty:
(ii.) Affecting consuls or other representatives of other countries:
(iii.) In which the Commonwealth, or a person suing or being sued on behalf of the Commonwealth, is a party:
(iv.) Between States, or between residents of different States, or between a State and a resident of another State:
(v.) In which a writ ofor prohibition or an injunction is sought against an officer of the Commonwealth:
the High Court shall have original jurisdiction. (ED - my bold)
SCORE - The Parliament is NOT higher authority here, it clearly says the High Court is the highest Authority wherever the Commonwealth is being sued, and specifically and in the first reference mentions Treaties. I cant see how they get around this - anyone?
76. The Parliament may make laws conferring original jurisdiction on the High Court in any matter--
(i.) Arising under this Constitution, or involving its interpretation:
(ii.) Arising under any laws made by the Parliament:
(iii.) Of Admiralty and maritime jurisdiction:
(iv.) Relating to the same subject-matter claimed under the laws of different States. This says the Parliament can give the High Court additional powers, but does not modify their rights under Section 75.
77. With respect to any of the matters mentioned in the last two sections the Parliament may make laws--
(i.) Defining the jurisdiction of any federal court other than the High Court: "other than the High Court", the Parliament cannot interfere with the rights granted to the High Court under Section 75
78. The Parliament may make laws conferring rights to proceed against the Commonwealth or a State in respect of matters within the limits of the judicial power. This is generally read as being subject to the limits set in Section 75, but we should look at Legal Precedent on this issue:
OK so lets look at some relevant High Court Precedent
Waterside Workers' Federation of Australia v J W Alexander Ltd  HCA 56; (1918) 25 CLR 434 (27 September 1918)
Chief Justice Griffith
"Sec. 71 of that instrument declares that "the judicial power of the Commonwealth shall be vested in a Federal Supreme Court, to be called the High Court of Australia, and in such other Federal Courts as the Parliament creates, and in such other Courts as it invests with Federal jurisdiction." This does not purport to be in itself a power, although it assumes the existence of a power to create new Federal Courts and to invest existing State Courts with Federal jurisdiction...
The provision of sec. 71 is, indeed, novel in the Empire, since the powers of other British legislatures are not limited by any such restrictions. It is, however, well known in the United States of America. Any inconvenience which may follow from giving effect to the express provisions of the Constitution cannot be considered in determining their meaning...
It is impossible under the Constitution to confer such functions upon any body other than a Court, nor can the difficulty be avoided by designating a body, which is not in its essential character a Court, by that name, or by calling the functions by another name.
In short, any attempt to vest any part of the judicial power of the Commonwealth in any body other than a Court is entirely ineffective."
New South Wales v Commonwealth (1915) 20 CLR 54 is a landmark Australian judgment of the High Court regarding judicial separation of power. It is also known as the Wheat Case.
The High Court of Australia decided that the strict insulation of judicial power was a fundamental principle of the Constitution. This also applies to tribunals and commissions set up by Federal Parliament which, can only recommend consequences.
Further the High Court held that only a court has judicial power under Chapter III of the constitution, so the Inter-State Commission created by Section 101 could not exercise judicial power despite the words of the Constitution, because it was set up by the executive and violated the conditions for being a Chapter III court.