Hi Barkley, since there is no weather station on the Whitney Summit, it is impossible to keep a log of the weather.
September and October weather on Whitney can be clear and dry, but occasional storms come through, especially the later in that period you go. And there is no specific period when the storms can be predicted at all, except for a few days in advance.
It sounds like you are planning a visit, so the best advice is to watch the forecasts (see the Weather Links above on the left) the few days before you come. If anything is predicted, I'd stay home.
It appears Whitney is having some unsettled weather at this time. Snow level around 13k, and there is significant cloud cover. I'm in Fresno, northwest of the summit, and there was a very unusual heavy overcast here all day.
The trip reports from people on the trail tonight will be quite interesting.