Welcome to the WhitneyZone, Heather.
I think the two most important things are the early date which means snow/ice is likely, and altitude acclimatization.
This year is shaping up as a little
above average for snow cover, so the 99 switchbacks part of the trail may not even be passable. In that situation, people climb the snow field just west of the switchbacks. And there, you want to go up early and get down before afternoon shadows set in and possibly ice up that area (which makes it much more dangerous).
You didn't say anything about high-altitude experience, so assuming you haven't been above 13,000 ft before, be sure you read up on what can happen (most often, headache and nausea). It REALLY helps to spend time, at least 24 hours at altitudes of 10,000 before the hike to let your body get accustomed to the elevation. Horseshoe meadows is usually the best place for that.
When it comes to deciding where to camp, lots of overnighters like to push to Trail Camp at 12,500 ft. But that can be a struggle with a full backpack. On the other hand, backpacking only to Outpost Camp can be easier, and still put you within reasonable distance of the summit. You sleep lower, so the altitude won't hit so hard -- maybe even increasing your acclimatization.
You have lots of people in your group, so tell them about this site, and especially the Orientation Notes link (above on the left).