In the Name of Allah, the Beneficent, the Merciful, and blessings and peace upon our master Muhammad, his family, companions and those who follow their noble way.
The Du’a of Qunut is considered from the encouraged (mandubat) actions of salah. Not from the the obligatory nor the emphasized sunnahs. It is recited silently prior to bowing (ruku’) in the obligatory prayer of Subh not the Witr nor the Sunnah of Fajr. [Dardir: Sharh Saghir]
If one forgets the Qunut prior to the ruku’ there is no problem in reciting it after raising from ruku’ prior to prostrating (sujud). However, one does not leave ruku’ and return to the standing position in order to recite it otherwise the prayer is invalidated. An obligatory (fard) action is not left to return to a sunnah or mundūb act. [Safti: Hashiyah Safti on al-Ashmawiyyah]
If the Qunut is forgotten or left out intentionally there is no prostration of forgetfulness (sujud sahwu) necessary and the prayer is sound. However, if one prostrates for forgetfulness intentionally for forgetting the Qunut (likewise other mandubat), in this case, the salah is invalidated due to intentionally adding to the prayer. [Safti: Hashiyah Safti on al-Ashmawiyyah]