I would recommend attempting Mt. Whitney with a professional guide service - not alone, with your limited experience. SMG, for example, is an excellent local guide service. They have a good local reputation.
http://www.sierramtnguides.com/A winter ascent of any big peak is a major challenge, and requires good training, equipment and, most of all, experience in those conditions.
A good starter climb might be something like Telescope Peak, near Death Valley. That would give you a little taste for what to expect on Mt. Whitney. Again, not alone, but with experienced companions.
While attempting Whitney in the winter, myself and friends (all experienced) came very close to being avalanched on the snow-shoeing hike in to Mirror Lake. On the occasion, we bailed out and opted to go to Telescope Peak.
