Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
There is no Shar`i (religious) basis for reciting Surat Al-Qadr after Wudu, and there is nothing in the Sunnah (teachings) of the Prophet (peace and blessings of Allah be upon him) to suggest this.
As-Sakhkhawi (may Allah have mercy on him) said: Reciting the Surah “Inna anzalnahu” [i.e., Surat Al-Qadr] after finishing Wudu is something for which there is no basis and this is not the Sunnah. End quote.
Al-`Amiri Al-Ghazzi (may Allah have mercy on him) said: Reciting Surat Al-Qadr after finishing Wudu is something for which there is no basis. (Al-Jadd Al-Hathith fi Bayan ma laysa bi Hadith, p.234)
Al-Albani (may Allah have mercy on him) mentioned in As-Silsilah Ad-Da`ifah (1449) a Hadith (narration) about this and he said concerning it: It is fabricated.
There are proven Du`as and Adhkar (words of remembrance) in the Prophet’s (peace and blessings of Allah be upon him) Sunnah which may be recited straight after doing Wudu . The Muslim should be keen to recite them and not add anything to them.
For more details, please see the following answers: 1180 , 11497 , 20850 , 21241 .
And Allah knows best.