Is the Udhiyah obligatory upon an unmarried, employed woman who lives in her parents' home, knowing that her father will offer the sacrifice? And what is her reward if she offers the sacrifice on her own behalf?

The Udhiyah (sacrifice) is a confirmed Sunnah according to the majority of scholars, and it is prescribed for anyone who can afford it, whether male or female. So, if you are able to afford its price without affecting your essential needs, then it is a Sunnah for you. If your father includes you in his Udhiyah while he is your provider, this is sufficient for him and for all his household, as the Prophet, peace and blessings be upon him, sacrificed two rams: one on behalf of himself and his household, and the other on behalf of those among his Ummah who affirmed the Oneness of Allah.