Is it permissible for a woman to slaughter an animal, and can the meat of an animal she slaughters be eaten?
Question

                My wife asked me an interesting question:Did any of the sahabiyyat ever slaughter an animal   during the `eid?Is this a proof that women can slaughter an animal if indeed any
  of the sahabiyyat slaughtered?
Praise be to Allah.The scholars of Islam are agreed that it is permissible 
  to eat the meat of an animal slaughtered by a woman, because of the general 
  terms used in the wording of the Qur’aan and Sunnah. Among the evidence 
  that it is permissible are the following:
The aayah in which Allaah says (interpretation of the meaning): 
    “Forbidden for you (for food) are: al-maytatah (dead animals – 
    cattle-beast not slaughtered), blood, the flesh of swine, and the meat of 
    that which has been slaughtered as a sacrifice for others than Allaah, or 
    has been slaughtered for idols, etc., or on which Allaah’s Name has mot 
    been mentioned while slaughtering, and that which has been killed by strangling, 
    or by a violent blow, or by a headlong fall, or by the goring of horns – 
    and that which has been (partly) eaten by a wild animal – unless you 
    are able to slaughter it (before its death)…” 
    [al-Maa’idah 5:3]. The evidence in this aayah is the phrase where 
    Allaah has permitted us to eat of any animal that we are able to slaughter 
    before it dies; this is general in application, and does not specify as to 
    whether the person who manages to do this is a man or a woman – so it 
    could be either.
 
  Al-Bukhaari (may Allaah have mercy on him) reported in his Saheeh 
    from ‘Ubayd-Allaah from Naafi’, that he (Naafi’) heard Ibn 
    Ka’b ibn Maalik narrating from his father that they used to have sheep 
    which they allowed to graze on the mountain of Sala’ in Madeenah: one 
    of the 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 of Allaah be upon him) or 
    I send someone to ask him. So he asked the Prophet  
    (peace and blessings of Allaah be upon him), or sent someone else to ask, 
    and he told him to eat it. ‘Ubay-Allaah said: “I liked the fact 
    that she was a slave-woman and she managed to slaughter it.”
  
 
Commenting on this hadeeth, Ibn Hijr (may Allaah have mercy on 
  him) said: “This shows that it is permitted to eat meat slaughtered by 
  a woman, whether she is free or a slave, old or young, Muslim or of the People 
  of the Book (i.e., Jewish or Christian), in a state of purity or otherwise, 
  because the Prophet  (peace and blessings of Allaah 
  be upon him) told them to eat the meat she had slaughtered and did not ask for 
  further details.”
This hadeeth also answers the question about whether any of the 
  Sahaabiyaat (female Companions of the Prophet  
  (peace and blessings of Allaah be upon him)) slaughtered animals.
The discussion above also makes it clear that a woman may slaughter 
  animals, because of the general terms used in the texts, and there is no difference 
  in this regard between meat slaughtered as a sacrifice or meat slaughtered for 
  regular food.
Shaykh al-Islam Ibn Taymiyah said: “It is permitted to eat from an animal 
  which a man or a woman slaughters Islamically before it dies, or from meat slaughtered 
  by a woman, even if she is menstruating, because her menstruation is not in 
  her hand. It is permissible to eat meat from an animal which a woman slaughters 
  Islamically before it dies, by the consensus of the Muslims.” (Al-Fataawa, 
  35/234).