When it comes to Maytag washers/dryers, 1965-1966 is two completely different eras. 1960-1965 was the 00/02 series. 1966-1974 was the 06 series. 1975-1980 was the 08 series. Not much changed on the 06-08 washers, but big changes occured on the dryers.
I believe the set you're referring to was turquoise 806's.
OK, I guess I should've known they'd change for the color year. The first year of I Dream of Jeannie, the black and white year, The Maytag set was all push button in 1965. What model is that one?
If the washer AND dryer were both had push buttons, then it would have been a A902/DE(or DG)750. If the washer that was push button only, than it was either a 160 or 900. The push button dryer didn't come along until 196/64, which was several years after the push button washer debuted.
In the early episodes they had a push button washer and dial dryer, then later got a push button dryer too. I wonder why they upgraded when apparently they never used them? They always had the same towels on the shelf above. I figured Granny used a washboard.