As Dan Bron notes in a comment beneath the posted question, and as KarlG reiterates in a separate answer, one fairly early match for "above [one's] pay grade" in the sense of "at higher level in the hierarchy than [one's] own is "[*Fiscal Year 1978 Authorization for Military Procurement, Research and Development, and Active Duty, Selected Reserve, and Civilian Personnel Strengths: Hearings Before the Committee on Armed Services, United States Senate, Ninety-fifth Congress, First Session, on S. 1210*](https://books.google.com/books?id=esoQAAAAIAAJ&q=%22above+my+pay+grade%22&dq=%22above+my+pay+grade%22&hl=en&sa=X&ved=0ahUKEwixwuvm_NfYAhXDnOAKHaRbDtE4ChDoAQhNMAc) (1977):

>Senator [Dale] BUMPERS: Who makes the final decision on whether Iran is going to get F14's and Phoenix missiles and so on? 
>
>Mr. ALLEN: Somebody way **above my pay grade**. 

The idiomatic use of "beyond [one's] pay grade" to mean above my level of skill or competence or decision-making authority goes back at least to the 1969 and 1971 instances first cited by muru and Phil Sweet, respectively, and subsequently compiled in Mari-Lou A's useful answer. My impression is that this expression and "above [one's] pay grade" are identical in their idiomatic meaning and may be used interchangeably, although an [Ngram graph](https://books.google.com/ngrams/graph?content=beyond+my+pay+grade%2Cabove+my+pay+grade&year_start=1950&year_end=2008&corpus=15&smoothing=0&share=&direct_url=t1%3B%2Cbeyond%20my%20pay%20grade%3B%2Cc0%3B.t1%3B%2Cabove%20my%20pay%20grade%3B%2Cc0) for 1950–2008 of "beyond my pay grade" (blue line) versus "above my pay grade" (red line) indicates the latter is the more common form.

The explicit association of pay grade with skill level (and so, implicitly, with level of competence and authority) in U.S. military jargon has roots that go back at least to 1954, when skill levels and pay grades appear as part of the standard nomenclature for categorizing job qualifications and appropriate salaries, as in U.S. Department of the Air Force, "[Enlistment and Reenlistment in Regular Air Force](https://www.google.com/search?q=%22pay+grade%22+%22skill+level%22&lr=lang_en&tbs=lr:lang_1en&tbm=bks&ei=EKxdWs32Funi0gKbsISICg&start=20&sa=N&biw=1080&bih=1049&dpr=1.2)" (1954). The two terms come together no later than in U.S. General Accounting Office, [*Decisions of the Comptroller General of the United States*](https://books.google.com/books?id=5gQ6ulizoXoC&pg=PA106&dq=%22pay+grade%22+%22skill+level%22&hl=en&sa=X&ved=0ahUKEwjzlLKE_dvYAhXilVQKHbpSA8oQ6AEIOzAD#v=onepage&q=%22pay%20grade%22%20%22skill%20level%22&f=false) (1959):

>Under section 209, an enlisted member may be awarded proficiency pay if he is found to have "special proficiency in military skill." This is interpreted as requiring a finding that the enlisted member either (1) is fully qualified in a critical military skill in the **pay grade** and **skill-level** in which he is serving, or (2) has demonstrated outstanding effectiveness in an assigned skill irrespective of its criticality. In this connection, it should be noted that in the armed forces the term "military skill" refers to a specific military specialty and **skill-level** within that specialty. Each **skill-level** normally has a direct counterpart in terms of military **pay grades**.  

So it is easy to see how even in the late 1950s military personnel might equate skill level with pay grade and use the terms (loosely) interchangeably. As for the issue of a task or responsibility or decision-making power being above an individual's skill level or pay grade, consider this excerpt from Edward Frederickson, U.S. Army Research Institute for the Behavioral and Social Sciences, [*Assessment Alternatives for a High Skill MOS: Final Report*](https://books.google.com/books?id=LENYAAAAYAAJ&q=%22periodic+evaluations+are+that+the+individual+continue%22&dq=%22periodic+evaluations+are+that+the+individual+continue%22&hl=en&sa=X&ved=0ahUKEwj5-fiAutnYAhUW42MKHStkAbsQ6AEIKTAA) (1975) [combined snippets]:

>Usually skill level correlates with pay grade. However, an individual may be awarded a skill level **above his pay grade**, but not below. This, in essence, indicates that an individual must be skill-qualified before he is awarded a promotion in pay grade. MOS [Military Occupation Specialty] and skill level qualifications are evaluated periodically using interviews, MOS evaluation tests, and performance appraisals and ratings. Decisions that can be made following these periodic evaluations are that the individual continue in his career progression, that he be reclassified to a lower skill level in the MOS, or reclassified to another MOS.

This excerpt indicates that the U.S. military made a serious, systematic effort to maintain a fundamental connection between pay grade and skill level. Although a soldier might on occasion be advanced to a skill level above his or her current pay grade (but not vice versa), the military's working assumption was that the pay grade would eventually catch up with the skill level. Here again, the practical connection between skill level and pay grade invites treating skill level (that is, competence and hierarchical authority) and pay grade as synonymous ideas and of using the latter term to stand for the former.

Thus, when U.S. soldiers or other military persons (and later, other government workers and private-sector workers) say that something is "above my pay grade," they may simply be saying that the thing in question falls into the purview of persons higher in the hierarchy than them—and thus at a different skill level or decision-making authority than theirs. And the examples of the idiomatic use of "above my pay grade" from 1960 and 1971 establish beyond reasonable doubt that it would not have been anachronistic for a character with a military background to say in 1971 (as the script of *The Post* has someone do) that something was above someone's pay grade.