Hi Erhard,
You’ve selected a great route. I suggest camping around Whitney Creek or Guitar Lake and packing everything up when you set out to climb Whitney in the AM. Most people drop their packs at the intersection near Trail Crest and continue on to the summit. You’ll return from the summit, pick up your pack, then continue on down via Mt Whitney Trail. Or, just carry your pack the whole time.
Temperatures will be cool during the day and cold at night. I suggest a 20 degree bag/quilt and a down/synthetic insulation jacket, knit cap, and tights for nights (and days, if needed). Check weather and forecasts here:
https://www.mountain-forecast.com/peaks/Mount-Whitney/forecasts/4418. Enjoy your trip, be safe!
TBird