Sam, there really isn't any period that is free of rain. But rain at Whitney Portal is infrequent. It CAN really dump, but there will be rain in the forecast before you go. You just need to take gear that will keep you dry just in case.
If the mountain is having clear skies and nothing is forecast then you can go with a minimum. My minimum is a plastic emergency bivy or parka. But if there is a possibility of rain, better gear would be a good idea.
