How Can a Menstruating Woman Observe Laylat al-Qadr?
Question

I was wondering what a woman can do on laylat al-qadr if she is menstruating at that time. Can she earn extra rewards for engaging herself in worship? If so, what is permissible for her to do on that night?
Praise be to Allah.A woman who is menstruating may do all acts of worship apart from praying, fasting, circumambulating the Ka’bah and doing i’tikaf in the mosque. 
It was narrated that the Prophet (peace and blessings of Allah be upon him) used to stay up at night during the last ten nights of Ramadan. Al-Bukhari (2401) and Muslim (1174) narrated that ‘Aishah (may Allah be pleased with her) said: “When the last ten nights of Ramadan came, the Prophet (peace and blessings of Allah be upon him) would refrain from marital relations, stay up at night and wake his family up.”  
Staying up at night is not only for prayer, rather it includes all kinds of acts of worship. This is how the scholars interpreted it. 
Al-Hafiz said: “Staying up at night ” means staying up to do acts of worship.” 
Al-Nawawi said: “Spending the night staying up to pray etc.” 
He said in ‘Awn al-Ma'bud: “I.e., in prayer, dhikr and reciting the Quran.”
Praying qiyam is the best act of worship that a person can do on Laylat al-Qadr. Hence the Prophet (peace and blessings of Allah be upon him) said: “Whoever spends the night of Laylat al-Qadr in prayer out of faith and in hope of reward, his previous sins will be forgiven.” (Narrated by al-Bukhari, 1901; Muslim, 760) 
Because the woman who is menstruating is not allowed to pray, she can spend the night in doing other acts of worship apart from prayer, such as: 
1- Reading or reciting Quran . 
2- Dhikr – such as saying Subhan-Allah , La ilaha illa-Allah, al-Hamdu Lillah, etc. She can repeat the words “Subhan-Allah wa’l-hamdu Lillah, wa la ilaha illa-Allah, wa Allahu akbar (Glory be to Allah, praise be to Allah, there is no god but Allah and Allah is Most Great)” and “Subhan Allah wa bi hamdihi, subhan Allah il-‘Azim (Glory and praise be to Allah, glory be to Allah the Almighty)” etc.
3- Istighfar (praying for forgiveness), by repeating the phrase “Astaghfir-Allah (I ask Allah for forgiveness).”
4- Du’a (supplication) – she can pray to Allah and ask Him for what is good in this world and in the Hereafter, for du'a’ is one of the best acts of worship. The Prophet (peace and blessings of Allah be upon him) said, “Du’a is ‘ibadah (worship).” (Narrated by al-Tirmidhi, 2895; classed as sahih by al-Albani in Sahih al-Tirmidhi, 2370).
 The woman who is menstruating can do these acts of worship and others on Laylat al-Qadr. 
We ask Allah to help us to do that which He loves and which pleases Him. May Allah accept our righteous deeds.