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.
It is impermissible for a Muslim wife to refrain from having intercourse with her husband without a valid excuse such as menses, illness, and the like. What the questioner mentioned is not a valid excuse to abstain from having intercourse with one's husband, since the Fajr prayer was not due yet, whereas obeying your husband and fulfilling his due rights over you is obligatory. Hence, you are not entitled to favor an act of worship that is not due and not yet obligatory over an already due and obligatory one. Moreover, it would be sufficient if you set the alarm so that you would be able to wake up for Fajr prayer, or ask someone to wake you up. However, if you could not wake up after all, there is no harm upon you; for sleep is an acknowledged excuse. Indeed, a sleeping person is exempted from obligations until he wakes up. Hence, all you need to do is to repent to Allaah, The Exalted, from the sin of disobeying your husband and abstaining from fulfilling his rights over you. You should ask for his forgiveness for what you have done in the past.
We beseech Allaah, The Exalted, to Guide you to that which He Loves and that pleases Him.
Allaah Knows best.