In this very comprehensive article on qurbani, the author states that it is proper for a woman to slaughter her own animal, and that in fact, if she is able to carry out the Dhabah (slaughtering) correctly, it will be better for her to sacrifice her own animal.
The following is the hadith of Rasool saws which supports that there is no prohibition against a female performing the slaughter of an animal:
ان امراة، ذبحت شاة بحجر، فسيل النبي صلى الله عليه وسلم عن ذلك، فامر باكلها
A lady slaughtered a sheep with a stone and then the Prophet (ﷺ) was asked about it and he permitted it to be eaten.
Al-Bukhari (may Allah have mercy on him) reported in his Saheeh from `Ubayd-Allah from Nafi`, that he (Nafi`) heard Ibn Ka`b ibn Malik narrating from his father that they used to have sheep which they allowed to graze on mount Sala’ in Madinah: a slave-women noticed that one of the sheep was dying, so she broke a stone and slaughtered it. He said: “Do not eat it until I ask the Prophet (peace and blessings be upon him) or I send someone to ask him. So he asked the Prophet (peace and blessings be upon him), or sent someone else to ask, and he told him to eat it. `Ubay-Allah said: “I liked the fact that she was a slave-woman and yet she managed to slaughter it.”
Commenting on this hadith, Ibn Hajar (may Allah have mercy on him) said: “This shows that it is permissible to eat meat slaughtered by a woman, whether she is free or a slave, old or young, Muslim or from the People of the Book (Jewish or Christian), in a state of purity or otherwise, because the Prophet (peace and blessings be upon him) told them to eat the meat she had slaughtered and did not ask for further details.”
This year, when Maulana summoned one of my children to perform the slaughter, Youngest shied away from the cow, stating that he preferred to start with a sheep. BD stepped forward and performed the slaughter herself. May Allah swt be pleased with her and accept her and our udhiyaa.