Firstly: 

It is not Sunnah to recite Qunoot in Fajr prayer all the time. We have explained that in the answers to question no. 20031 and 5459. 

Secondly: 

Your prayer behind an imam who recites Qunoot in Fajr is valid, but if there is someone who does not always recite Qunoot in Fajr, it is better to pray behind him, so as to follow the Sunnah. 

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said concerning some matters of ijtihaad in which the scholars differed, such as Qunoot in Fajr and Witr: 

The scholars are agreed that if a person does both, his worship is valid and there is no sin on him, but they disputed [?] concerning which is better and what the Prophet (peace and blessings of Allaah be upon him) used to do. With regard to the issue of reciting Qunoot in Fajr and Witr, the issue of whether the Basmalah should be spoken out loud, and the issue of the words used to seek refuge with Allaah and so on ... They are agreed that if a person says the Basmalah out loud, his prayer is valid, and if a person says it silently his prayer is also valid; and that if a person recites Qunoot in Fajr his prayer is valid and if he does not recite it his prayer is valid, and the same applies to Witr. 

He also said (23/115): 

From what we have mentioned it is clear that Qunoot is to be recited at times of calamity… whoever says that it is an essential part of prayer which may be made up for with the prostration of forgetfulness is basing that on the idea that it is a sunnah which is to be done all the time, like the first tashahhud and so on. But it is clear that this is not the case; it is not a Sunnah that is to be done regularly, and no prostration of forgetfulness is required if it is omitted. If some believe that it is a regular Sunnah based on their own ijtihaad this is fine, as in the case of all other issues of ijtihaad. Hence the person who is praying behind an imam should follow his imam in issues where there is room for ijtihaad. So if he recites Qunoot he should recite it with him, and if he does not recite Qunoot he should not recite it. The Prophet (peace and blessings of Allaah be upon him) said: “The imam has been appointed to be followed.” And he said: “Do not differ from your imams.” And it is proven in al-Saheeh that he said: “They lead you in prayer; if they get it right (the reward) is for you and for them, and if they get it wrong, (the reward) is for you and (the sin) is on them.” 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: We have an imam who recites Qunoot in Fajr prayer all the time; should we follow him? Should we say Ameen to his du’aa’? 

He replied: 

Whoever prays behind an imam who recites Qunoot in Fajr prayer, let him follow the imam in Qunoot in Fajr prayer, and say ameen to his supplication. This was stated by Imam Ahmad (may Allaah have mercy on him). 

Majmoo’ Fataawa Ibn ‘Uthaymeen, 14/177 

The Standing Committee was asked: Is it permissible to pray behind an imam who holds his arms at his sides in his prayer and always recites Qunoot in the last rak’ah of Fajr prayer? 

They replied: Putting the right hand over the left when praying is Sunnah, and holding the arms at the sides is contrary to the Sunnah. Always reciting Qunoot in the last rak’ah of Fajr prayer, as some of the Maalikis and Shaafa’is do, is contrary to the Sunnah because there is no proof that the Prophet (peace and blessings of Allaah be upon him) did that. Rather he used to recite Qunoot at times of calamity, and he used to recite Qunoot in Witr prayer. If the imam holds his arms at his side when praying and always recites Qunoot in Fajr prayer, as mentioned in the question, then knowledgeable people should advise him and remind him to follow the Sunnah. If he responds, then praise be to Allaah, but if he refuses and it is possible to offer prayers in congregation behind someone else, you should pray behind someone else so as to adhere to the Sunnah. But if that is not possible then you should pray behind him so as to keep the jamaa’ah (congregation) together. The prayer in valid in either case. 

Fataawa al-Lajnah al-Daa’imah, 7/366 

And Allaah knows best.