It is recommended to send the weak among women and others ahead from Al-Muzdalifah to Mina at the end of the night, before it gets crowded, but it is recommended for others to stay there until they have prayed Subh in Al-Muzdalifah

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 (ﷺ) had granted permission to women.