I am due to have a caesarean section to deliver my baby, Insha Allah, on the 13th Aug. and I was wondering, would it be allowed for me to have a copy of Qur'an or a Du'a book I can read while this operation is taking place.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The questioner sister may carry the Qur'an and recite it wherever she goes, even in the operation theater provided she is in the state of complete purity that allows her to recite and touch the Qur'an. Allah Says (interpretation of meaning): {That (this) is indeed an honourable recital (the Noble Qur'ân). In a Book well-guarded (with Allâh in the heaven i.e. Al-Lauh Al-Mahfûz). Which (that Book with Allâh) none can touch but the purified (i.e. the angels).} [56: 77-79].
The Prophet (Sallallahu Alaihi wa Sallam) said: "No one should touch the Qur'an except a pure person" [Reported Imams Muslim and Abu Dawood ].
Ali (Radiya Allahu Anhu) said: "Nothing could prevent the Prophet from the Qur'an except the state of ritual impurity" [ al-Tirmizi and others].
The above ruling is only for the handling the Qur'an; it does not apply to a book of supplication. However, such a book should not be placed in an impure place, same as the Qur'an, especially if it contains verses from the Qur'an or the Hadith.
Allah knows best.