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 is His slave and Messenger.
Anas narrated that the Prophet said: “Whoever prays the Fajr prayer in congregation and then he remains sitting mentioning Allaah until the sun rises, and then he prays two Rak’ahs, will receive the reward of one Hajj and one ‘Umrah, complete, complete, complete.” [At-Tirmithi with a good chain of narrators]
The Hadeeth proves the merits of performing Fajr prayer in congregation and sitting there till the sun rises and then praying two Rak'ahs.
The mentioned virtues are general hence including anyone who performs Fajr prayer in congregation and sits till the sun rises and then performs two Rak’ahs.
There is no doubt that if a woman does so in her house, she will get a great reward. However, we do not have any evidence that proves that she will get the reward of a Hajj and 'Umrah. Despite that, we hope that Allaah will grant her that reward as long as she remains in her prayer place till sunrise mentioning Allaah. We hope so since the Prophet said that the prayer of a woman in her house is better than her prayer in a mosque.
Allaah Knows best.