I try to do Whitney twice a year - spring and fall - and the fall dates for the last four years are 9/12/07, 9/25/08, 9/28/09 and 9/15/10. Living nearby, I keep my eye on the weather and go before the first major storm. In a least 2 of those years, that storm occurred within a week or so after those dates. Does the first storm shut the mountain down? That all depends - if you live in a snowy climate, then it's probably no big deal. OTH, if you've never hiked in snow before, maybe it is.

Hopes this helps in terms of dates and planning.