Thats the best month to go . I went on early Sep to Leh. Temp are normal, carry one jackets. Nights and mornings are colder in Nubra and Pangong. If you are staying in Pangong in tent, please carry good thermals as the temp goes down below 8 /7 degree. The stars are clear, very less rains, may get little landslides.
My favourite time of the year to Travel to Leh. All my three trips to Leh was during the first week of September. September in fact is the best time to visit Leh Ladakh. The roads will be in perfect condition, there is greenery all around, the lakes will look aqua blue in colour and what more to ask.