There is no specific du’aa’ to be recited before reading Qur’aan
Question

                Is there any specific duaa before reading / memorizing the Quran? Do we have to have wudu to touch the Quran? And must we cover our aurah (i.e the whole body inc. head cover for women) before we can read the Quran? Or can she just dress accordingly in her normal house clothes without the head cover?
Praise be to Allah.
    There is no specific du’aa’ mentioned in the Qur’aan or 
    Sunnah, or in the reliable books of du’aa’s and dhikr, or in the opinions of 
    the reputable scholars, that is to be recited before reading or memorizing 
    Qur’aan. Rather what is prescribed is to seek refuge with Allaah from the 
    accursed Shaytaan before reading, because Allaah says (interpretation of the 
    meaning): 

    “So when you want to recite the Qur’aan, seek refuge with 
    Allaah from Shaytaan (Satan), the outcast (the cursed one)”

    [al-Nahl 16:98]

    If a person makes du’aa’ at any time, asking Allaah to make 
    it easy for him to memorize Qur’aan or to enable him to understand what he 
    has learned by heart, or any appropriate du’aa’ that he wants to say, 
    without adhering to a particular time for reciting this du’aa’, then there 
    is nothing wrong with that. 

    With regard to the obligation of having wudoo’ before 
    touching the Qur’aan, you will find the answer to this question under 
    question no. 10672. 

    It is not necessary to cover the parts of the body that you 
    cover in prayer in order to read Qur’aan, so it is o.k. to read Qur’aan 
    wearing regular clothes, without covering the head. 

    Shaykh Ibn ‘Uthaymeen said in his discussion on sujood 
    al-tilaawah (prostration required when reading certain aayahs of the 
    Qur’aan): “Sujood al-tilaawah should be done as soon as one reads it in the 
    Qur’aan, so it is o.k. to do sujood in any condition, even bareheaded etc., 
    because this prostration does not come under the same rulings as prayer.” 
    (1/249) 

    From his words it may be understood that there is nothing 
    wrong with a woman reading Qur’aan with her head uncovered, because she will 
    only read an aayah where a prostration is required when she is reading 
    Qur’aan, so she will be reading it with her head uncovered. The Shaykh did 
    not explain to us whether her head may be uncovered when reading Qur’aan.
    We advise you to strive to venerate and respect the Qur’aan, and read it with care, focusing on the meanings, at any time and in any circumstances, whatever is easy for you. The fuqaha’ stated that it is o.k. to read Qur’aan in all circumstances, standing or sitting, sitting cross-legged or otherwise, lying down, riding or walking, because of the hadeeth of ‘Aa’ishah (may Allaah be pleased with her) who said: “The Prophet  
    (peace and blessings of Allaah be upon him) used to lie down with his head in my lap when I was menstruating, and he would recite Qur’aan.” Narrated by al-Bukhaari, 297; Muslim, 301.