Mazal tov on the bat mitzva and on this wonderful achievement!
According to the Talmud, the world’s continued existence depends on responding to kaddish after learning words of aggada, non-halachic sections of Oral Torah (Sota 49a). Interestingly, the focus here is on responding to the kaddish, not reciting it.
Kaddish de-rabbanan, recited at the completion of any Torah study with a minyan present, includes a prayer for the flourishing of rabbis and students of Torah. An extended version of this kaddish, recited only at a siyyum, refers to the upcoming redemption, including revival of the dead, rebuilding Yerushalayim, restoring the monarchy and the coming of Mashiach. This kaddish can be recited by someone other than the person who is making the siyyum, even if the person reciting kaddish did not participate in any way in the study (Mishna Berura 54:9).
We plan to discuss the halachot of a woman reciting mourner’s kaddish in a future article on Deracheha. There is a range of halachic opinion on the matter, and practices differ from synagogue to synagogue. In some, women do not recite kaddish, in others women recite kaddish along with a man, and in others a woman recites kaddish on her own. In theory, the question of a woman reciting kaddish at a siyyum should be treated with greater leniency than mourner’s kaddish, since a siyyum is generally not held in a synagogue. On the other hand, mourner’s kaddish is unique among kaddishes, due to the importance of the relationship between the mourner and the deceased, so we cannot be sure that halachic decisors would extend their rulings on mourner’s kaddish to another realm. This specific question about kaddish at a siyyum has not yet been heavily discussed in halachic literature.
Rav Aharon Lichtenstein maintained that it was technically permissible for a woman to recite kaddish alone at a siyyum, but that whether or not it should actually be done in a given setting would depend on the setting and on communal sensitivities and practice. For example, in Alon Shevut he permitted a woman to recite kaddish on her own at a private siyyum held at her home with ten men present, but advised a couple asking about their daughter reciting kaddish at her bat mitzva that that would be more of an issue, since it would be more public. Kaddish at a public celebration may more closely resemble recitation by a prayer leader at synagogue.
At Beit Midrash Migdal Oz, women do not recite kaddish when making a siyyum. Rav Lichtenstein’s daughter, Rabbanit Esti Rosenberg, had her father recite the kaddish at the siyyumim made at all of her children’s bar or bat mitzvahs, in order to emphasize to all of her children that their learning was part of a heritage across generations.
In your case, we suggest that you consult with your local rabbinic authority, taking into account both the accepted practice in your community regarding mourner’s kaddish and how private your affair will be.