Your dates are fine, i climbed on 29/30th in 2010! The weather should still be very warm at that time (i climbed in shorts) but pay attention to weather reports.
There was thousands of people climbing the night i did, so you will be fine climbing alone.
If the weather is good wear a light set of clothes with some warmer ones to wear when it gets cold, and bring a second set to store in a locker at the 5th station as the decent is very very dusty.
A good pair of boots is essential with good ankle protection, and don't forget a head-light.
Enjoy your climb.