There is not really an issue with finding a spot to camp.
In terms of time, there is no real need for an early start.
It is 6 miles, about 4k elevation gain. Most easily do it in 6 hours, but it is good to leave a margin if you don't know the mountain. Especially if you have not followed an acclimatization schedule. It is now getting dark after 8p.
So, noon is a [b]very[/b] comfortable timeframe.
Personally, I like to hike when it is cooler, though.
