Hi,
Since the official release date for the Nintendo NES Action Set (which replaced the NES Deluxe Set which had the Zapper, R.O.B. and 2 separate Game Paks that are Duck Hunt and Gyromite) on Wikipedia and many other sources (incl. NES World), and the 2-in-1 Game Pak that is Super Mario Bros./Duck Hunt is listed as November 1988, I find that to be wrong because I distinctly remember getting mine during the spring of that year. The release date for the NES Action Set with the two-tone grey Zapper gun would actually be January or February 1988.
This also leads me to ask you whether or not the very first NES Action Sets have the 1985 version of the Nintendo quality seal which reads "This seal is your assurance that Nintendo has approved and guaranteed the quality of this product." Later in 1988, the seal's text was changed slightly, with the words "approved and guaranteed" replaced by "evaluated and approved." Then, in 1989, the seal changed again, this time using an oval starburst with a white background, with the text "Official Nintendo Seal of Quality."
The very first NES Power Sets - that is, the bundle with the Zapper and the Power Pad - would have begun with the 2nd seal used.
~Ben