Should I perform the voluntary prayer before the obligatory prayer if time is limited with regards to Fajr?

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.

If the case is as described by the questioner, he should start with the obligatory prayer in order not to miss its specified time; then, if there is still time remaining, he may perform the voluntary prayer. Otherwise, he may perform the voluntary prayer after sunrise. Abu Hurayrah, may Allaah Be Pleased with him, narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: "Whoever did not perform the voluntary prayer of Fajr should perform it after the sun rises." [At-Tirmithi, Al-Haakim and Ibn Hibbaan who said it is Saheeh] Moreover, the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, saw a man praying two Rak‘ahs after the Fajr prayer; so he said: "The Fajr prayer consists of two Rak‘ahs." The man said: "I had not  performed the two voluntary Rak‘ahs before it so I performed them now." The Prophet, sallallaahu ‘alayhi wa sallam, did not comment. [At-Tirmithi, Abu Daawood and Ibn Maajah]

Allaah Knows best.