All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Making Qunoot in the Fajr prayer is a controversial issue, about which the Companions and the Tabi‘oon held different opinions, as did the scholars who succeeded them. Therefore, it is permissible for this Imaam to make Qunoot. If he does not do so, then it is permissible for the worshipers who view its validity to make it if they know that they would most likely catch up with the Imaam in prostration.
It is said in Kifayat Al-Akhyar, a book on the Shaafi‘i school of Fiqh:
"If an Imaam left out the Qunoot, either for not viewing its validity, like a Hanafi, or out of forgetfulness, the person praying behind him should not make Qunoot if he knows he will not catch up with the Imaam in prostration if he makes it. But if he knows he will catch up with the Imaam, then he can make Qunoot."
This applies to the case of one led in prayer by an Imaam who does not make Qunoot. However, an Imaam who does not view the validity of Qunoot in the Fajr prayer is not required to wait for those praying behind him until they make it. If he does this anyway, he should not remain silent. Rather, he should either make Qunoot, and there is nothing wrong with this, or busy himself by reciting the reported supplication that is to be said after rising from bowing.
Allaah Knows best.