When a woman is in the state of haydh, it is mustahab for her to do wudhu, sit on the prayer mat and recite zikr. This wudhu however does not allow her to touch the writing of the Qur'an. In regards to reciting duas and Quran, there is no problem. If it is said that it is makrooh to recite the Qur'an, it means the rewards are less. However the wajib sajda verses of the Qur'an should not be recited.