I used to live in Inyokern for several years, and Whitney Portal was about 90 minutes away so I had the opportunity to summit many times (17 thus far) and did shorter hikes to Trail Camp many times. Of the times I summited, 7 of them were in September.
John mentioned several reasons why September is a good month, and I'd add that in general the typical hiker that time of year tends to be older and more experienced.
While the weather in September is fairly stable, and the chance of a sudden t-storm unusual, it's likely that the section with cables may have a bit of ice build-up due to colder nights and lack of sunshine in that particular section. This ice is nearly always easy to avoid by rock-hopping, and its existence will be well-noted by the frequent trip reports posted either here or on the Whitney Portal BB. Also, do watch the weather forecasts carefully, because it seems that there will be at least one storm in late September that will dump a few inches, sometimes more. Often this snow melts in a few days, but it signals the transition to more winter-like conditions. Summiting is generally easier - at least for me - before this transition storm rather than after.
