It is certainly more correct to pray individually before Netz HaChama (sunrise) than to wake up for the later minyan. Granted, you will be praying without a minyan, but Maran the Shulchan Aruch (beginning of Siman 89) ruled that one who is under duress (anus) or facing an exigent circumstance (b’shas hadchak) may pray Shacharis after Alos HaShachar, prior to Netz HaChama. Furthermore, Maran my great-uncle HaGaon Rav Yosef Shalom Elyashiv ztz”l (Tefillah Kehilchasah, Ch. 3, note 63) ruled that performing labor before praying carries a prohibition, and it is preferable for such a person to pray individually before Alos HaShachar. Therefore, the law is the same in this scenario, especially since there is a real concern that while asleep, you might miss the designated time for Kriyas Shema, and perhaps even the time for Tefillah altogether.

However, one must be careful to don the Tallis and Tefillin only after the time of Misheyakir (when there is enough daylight to recognize a familiar acquaintance), which is approximately 50 minutes before Netz HaChama. In other words, you should begin your prayers—Birkos HaShachar and Pesukei D’Zimrah up until Yishtabach—and the moment this time arrives, don your Tefillin between Yishtabach and Yotzer, continuing with them until the conclusion of the Tefillah. Ex post facto (b’di’avad), if you cannot wait until this time, it is permitted to pray with the Tallis and Tefillin donned prior to Misheyakir without reciting the blessings; after donning them, you should touch the Tallis and Tefillin at the proper time, recite the blessings over them, and read Kriyas Shema while wearing them (Igros Moshe, Part 4, Siman 6; Cheshev HaEphod, Part 2, Siman 143).