Sahih Muslim Book 7, Hadith Number 2962.

Chapter : It is excellent that the aged and the weak, especially among the women, should hasten from Muzdalifa to Mina at the latter part of the night before the people moving in multitude. and excellence of staying there for others until they observe the dawn prayer at Muzdalifa.

Abdullah, the freed slave of (Hadrat) Asma’, reported: Asma’ (Allah be pleased with her), as she was in the house at Muzdalifa, asked me whether the moon had set. I said: No. She prayed for some time, and again said: My son has the moon set? I said: Yes. And she said: Set forth along with me, and so we set forth until (we reached Mini) and the stoned at al-Jamra. She then prayed in her place. I said to her: Respected lady, we set forth (in the very early part of dawn) when it was dark, whereupon she said: My son, there is no harm in it; Allah’s Apostle (may peace be upon him) had granted permission to women. This Hadith has been narrated by Ibn Juraij with the same chain of transmitters, and In his narration (the words are): “She (Asma’) said: My son, Allah’s Apostle (may peace be upon him) granted permission to women.”