It is not correct to make qunut in the dawn prayer except during times of calamity, in which case it may be made in any of the five daily prayers. Abu Malik al-Ashja’i said: “My father prayed behind the Prophet sallallahu alehi wasallam when he was sixteen years old, and he prayed behind Abu Bakr, ‘Umar, and ‘Uthman. I asked him, ‘Did they make the qunut?’ He said, ‘No, son, it is something that has been innovated.”‘ This is related by Ahmad, an-Nasa’i, Ibn Majah, and at-Tirmizhi who calls it sahih. Anas said that the Prophet sallallahu alehi wasallam would not make the qunut in fajr unless he was supplicating for a people or supplicating against a people. This is related by Ibn Hibban, al-Khatib, and Ibn Khuzaimah who said it is sahih.
It is also related that az-Zubair, Abu Bakr, ‘Umar, and ‘Uthman did not make the qunut in the dawn prayer. This is the opinion of the Hanafiyyah, the Hanbaliyyah, Ibn al-Mubarak, al-Thauri, and Ishaq. The followers of Shaf’i are of the opinion that the qunut is to be made after the ruku’ of the second rak’ah in the obligatory dawn prayer. This opinion is based on the following two reports. Ibn Sireen narrates that Anas ibn Malik was asked: “Did the Prophet make the qunut in the dawn prayer?” He answered: “Yes.” They asked him: “Before the ruku’ or after it?” He replied: “After it.” This is related by the group save at-Tirmizhi.
There is a report from Anas which says: “The Messenger of Allah sallallahu alehi wasallam did not stop making qunut during the dawn prayer until he left this world.” This is related by Ahmad, al-Bazzar, adDaraqutni, al-Baihaqi, and al-Hakim who says it is sahih.
However, there remains some doubt concerning this evidence since the qunut which they asked Anas about, as is clear in the narrations of al Bukhari and Muslim, was the qunut during the time of calamities. Concerning the latter hadith (the one mentioned in support of their stand), in its chain of narrators there is Abu Ja’far ar-Razi who is not a credible source and, thus, one cannot build a case upon his hadith. How could it be that the Messenger of Allah never stopped performing this qunut until his death, and yet, the rightly guided caliphs did not perform it? It is even confirmed that Anas himself did not make the qunut in the dawn prayer! If we must accept this latter hadith as authentic, it would mean that the Prophet always made supplications and remembrance (zhikr), after the ruku’, until his death. This would also come under qunut and, in this sense, it would be more befitting. Still, this is one of the matters in which it is acceptable to have differences of opinion, and one may either do it or leave it. The best guidance is that of Muhammad sallallahu alehi wasllam.