Wa alaikum al-salaam wa rahmatullahi wa barakatuh.
The acts of ṣalāh are divided into two categories: integrals (arkān) and recommended (nawāfil/sunan). The recommended acts are further divided into two types: ʾabʿādh and hayʾāt.
The ʾabʿādh are a specific set of recommended acts that do not invalidate the prayer but if any of them are not performed, it is recommended to do sujūd al-sahw. The hayʾāt include all other recommended acts of ṣalāh, and if any of them are not performed, the ṣalāh is valid and sujūd al-sahw is prohibited.
The qunūt is included in the ʾabʿādh for the fajr prayer throughout the entire year, as well as the witr prayer during the second half of ramadhān only.
Based on the above mentioned, your fajr prayer is valid if you do not perform qunūt, but it is recommended for you to do sujūd al-sahw.
Allah knows best.
Answered by: Shaykh Omar Mohsin