The relevant section provides
(1) This Act does not apply to any request for access to a document of the Official Secretary to the Governor-General unless the document relates to matters of an administrative nature.
(2) For the purposes of this Act, a document in the possession of a person employed under section 13 of the Governor-General Act 1974 that is in his or her possession by reason of his or her employment under that section shall be taken to be in the possession of the Official Secretary to the Governor-General.
the status of the Office under the FOI Act is analogous to that of courts and certain tribunals. Under s 5 (for courts) and s 6 (for certain tribunals), the FOI Act does not apply to any request for access to a document of a court/tribunal unless the document relates to matters of an administrative nature.
The FOI Act provides in similar terms that it only applies to the Official Secretary to the Governor-General in respect of requests for access to documents that relate to ‘matters of an administrative nature' (s 6A). Implicitly, the Act does not apply to requests for access to documents that relate to the Governor-General's discharge of official functions conferred by the Constitution or an enactment.
17. ... the documents that the applicant has sought that contain detail about specific nominations and how those nominations were processed do not, in my view, relate to matters of an administrative nature for the purposes of s 6A. They relate to a core vice-regal function: deciding whether or not to appoint an individual to the Order of Australia.18. This is also true of the other documents that the applicant sought: manuals and guidelines relating to the administration of the Australian honours system, and documents relating to review processes. These documents, like the ones relating specifically to the applicant's nominations, relate to the Governor-General's discharge of a core function, namely the vice-regal honours function. As explained in the Guidelines, the FOI Act implicitly does not apply to requests for access to such documents. These documents do not relate to matters of an administrative nature within the meaning of s 6A of the FOI Act.
The section has not been subject to judicial interpretation, although the same term is used in sections 5 and 6 regarding documents held by courts and tribunals and has been the subject of several decisions that focus on the meaning in the context of the independence of such bodies. What s 6A means is another matter, but similar issues may arise particularly regarding documents that relate to a particular nomination for an Order of Australia award.The Official Secretary of course also has available all the exemptions in the FOI act.
In Bienstein v Family Court of Australia  FCA 1138 Justice Gray [at 46] quoted the Hansard from 1981 when the act was amended in response to a committee recommendation to include sections 5 and 6:
The kind of matters that the Committee had in mind as justifying the operation of the Bill were questions relating to the number of sitting days, the number of cases determined, the number of cases withdrawn, the number of cases which were subsequently appealed, criminal cases in which bail was awarded and so on.... The Senate Committee does not see this as interfering or trespassing in any way with the independence of these bodies which, as a part of our constitutional system, it is important to preserve. It is a distinction which is familiar and understood and the language in which the amendment is cast is sufficiently clear and precise, in our view, to be accommodated directly by the GovernmentJustice Gray went on to note 
The wording is identical to that used in s 5, but s 6 relates to institutions that are not judicial, in the sense that they are not created under Ch III of the Constitution and are therefore emanations of the Executive arm of government, required to be entirely separate from the judicial arm. Having said this, the independence of those institutions from interference by the Executive arm of government is also important. The then Attorney-General recognised this in the course of the Senate debate. Having regard to the nature of both courts and the institutions to which s 6 applies, and to the importance of judicial independence, and the independence of the other institutions, recognised on both sides of the Senate debate about the amendment, it can be taken that both s 5 and s 6 are intended not to extend as far as requiring the giving of access to documents that would put that independence at risk."Justice Gray declined to follow Western Australian decisions based on the dictionary definition of the word "administrative", meaning "concerning or relating to the management of affairs," where the words were confined to documents relating to the management of the affairs of a court or tribunal, excluding documents "created in the course of and for the purpose of particular matters dealt with by the agency in the exercise of its adjudicative functions." (Although not cited this decision of Chief Justice Martin in the Western Australian Supreme Court outlines the narrower WA interpretation.) Justice Gray  said this approach "would constrain unduly the operation of the phrase "relates to matters of an administrative nature." It should not be followed in relation to s 5 of the FOI Act." Leading to this conclusion:
..clearly.. s 5 of the FOI Act should be interpreted so that access to documents relating to the exercise of the judicial functions of courts, and to the decision-making functions of tribunals, are not excluded from the right of access merely for that reason. What emerges from the context of s 5, as well as from the extrinsic materials, is a concern that documents the revelation of which would impinge upon the independence essential to the exercise of the judicial function, or the decision-making process, should not be made available. It follows that, while the words "relates to matters of an administrative nature" in s 5 (and also in s 6) should be interpreted as including documents that bear upon the exercise of the judicial, or decision-making, functions, only those documents the availability of which would not impinge upon the necessary independence should be regarded as documents relating to matters of an administrative nature. The test will not necessarily be easy to apply. Its application will depend upon the terms of the request for a document, and may require an examination of the circumstances in which the document was produced and is retained. In the application of the test, however, it is necessary not to take too strict a view of what is necessary to be kept confidential in the interests of preserving the independence of the judicial and administrative decision-making functions.