Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Reading surat al-Qadr after wudu was not prescribed by the Prophet (peace be upon him) and hence it amounts to be an innovation, especially if someone thinks it is part of wudu.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Offering prayer the Prophet’s way
The Prophet (peace be upon him) told us, “Pray as you have seen me praying.” (Ibn Hajar)
Even as he wanted his companions to pray as he prayed, he also wanted to perform wudu (ablution) as he did. Thus, narrations tell us that once he ordered a bucket of water, he demonstrated wudu, and the companions learned it from him. In the same way, he advised them to perform the rites of Hajj as he did.
It is nowhere mentioned anywhere in the sources that he ever told his companions to recite surat al-Qadr after performing wudu.
Duaa after wudu
When we closely examine the traditions, we find that he ordered them to start wudu by invoking the name of Allah (i.e., saying bismillah). And in other reports, we also that he advised us to read the following duaa after completion of wudu:
Ashhadu an laa ilaaha illa Allah wa ashhadu anna Muhammadan rasoolulla
(I bear witness there is no god but Allah; I also bear witness that Muhammad is the messenger of Allah) (Muslim)
And in another version (reported by Imam At-Tirmidhi), the following is added:
Allaahumma ij’lnee mina al-thawwaabeena wa ij`lnee mina al-mutatahhirren
(O Allah, make me among those who are ever turning to You in repentance. And make me among those who are constantly engaged in acts of purification).
Is it recommended to read surat al-Qadr after wudu?
We believe that the Prophet (peace be upon him) has transmitted to us all the essentials of religion without adding or taking away from it. We are also convinced that his companions have passed on the methods of prayer and wudu as he taught them.
Since none of them reported that we should read surat al-qadar after wudhu, we can safely conclude that it is prescribed by the Prophet (peace be upon him) and hence it amounts to be an innovation, especially if someone thinks it is part of wudu.
Almighty Allah knows best.