I wrote some short surahs in my notebook for the purpose of memorizing it while I have free time. Now, I have menstruation. Since it is not a real Quran, am I still allowed to touch and open my notebook wherein the Word of Allah is written?

Most scholars have prohibited menstruating women and people in a state of sexual defilement (janābah ) from reciting the Qur’ān or touching it. However some of them are of the opinion that she can recite the Qur’ān without touching it except with her hand covered. IbrāhĪm al-Nakha‘i said, "There is no harm on menstruating woman reciting a Qur’ānic verse." It was also the opinion of al-Imām Mālik [Fatḥ al-Bāri] and this is the strongest opinion. Other scholars allowed touching the mushaf for menstruating women if there is a need, because it is recommended to have wudoo' before touching the mushaf, but not obligatory, and this is the opinion that I support.

The menstruating woman is allowed to mention Allah. Umm ‘Aṭiyyah reported that they were instructed to let the menstruating women come out for the ‘Īd s and say "Allāhu Akbar" (Allah is the Greatest). 
(al- Bukhāri quoted this anecdote to show that since menstruating women were instructed to speak Allah's Names and His Attributes, they should also be allowed to read the Qur’ān, in which Allah's Names and Attributes are also mentioned.)

Touching the notebook in which verses of Qur'aan are written, or books or tafsir, or an electronic device with the Qur'an on it, will not take the same ruling as a mushaf, as those things are not considered a mushaf.

Ibn ‘Abbās quoted Abu Sufyān as saying, "Heraclius asked for the letter from the Prophet and read it. It began: In the name of Allah, the Beneficent, the Most Merciful. "O people of the Scripture, let us come to a common principle between us, that we do not worship anyone (or anything) besides Allah." (al-Bukhāri).