Here is an even earlier attested use:

(May 13, 2005 e-mail response from Richard Stratton)
Barry,

The most unique request I have received since 1973!

Etymology of "whole nine yards"?

1. Where first heard?
Navy School of Preflight in July 1955 at the ACRAAC (Aviation Cadet Recreation and Athletic Club - a base beer hall; NavCad's could not use O Club). Home of salacious & scatological songs, shaggy dog stories and off beat humor.
2. What meaning then?
Referred to the mythical Andy McTavish's private member and the scarf knitted by him for the birthday of his affianced, Mary Margaret MacMuff.
3. Explained in detail?
Yes, in great detail. One of a series of stories and songs enshrining the courtship of Andy and Mary Margaret.
4. US or VN?
United States - NAS Pensacola FL
5. Aviator usage in 1973?
The "whole nine yards" joined "the whole kit and caboodle" as meaning "all inclusive", "containing each and every element" and "a whole without any exceptions". It had lost all sexual reference or innuendo.

The attachment--the long story of Andrew MacTavish and Mary MacMuff--can be found here.