If a women would like to say the prayer of Kiddush Levana is she allowed to say it with a brocha? (not together with men)
Excerpts from this blog entry:
The gemara (Sanhedrin 42a) describing kiddush levana, states regarding women:
אמר ליה רב אחא לרב אשי: במערבא מברכי ברוך מחדש חדשים, אמר ליה: האי - נשי דידן נמי מברכי
The basic implication of the gemara seems to be that although women recite a shorter beracha, they do say something. Similarly, the Meiri quotes the gemara almost verbatim, and Rav Ovadiah Yosef (Shu"t Yabi'a Omer OC 5:36) proves that according to the Meiri, women should say the short version:
ומוכח דלקושטא דמילתא הוא, שהנשים מברכות בר' הלבנה בקיצור
Yet, the minhag seems to have evolved that women do not say kiddush levana
Several reasons given in this article, but the two that makes most sense to me are:
2) Maharam Shik (Shu"t, OC #90) - When to say kiddush levana is based upon figuring out the calendar, and this was a skill performed only by men.
4) Magen Avrohom (OC 296:11) - Has difficulty understanding (and ultimately disagrees with) the Rama that women cannot make their own havdalah, but should rather hear their husbands'. However, he suggests (for the Rama) that perhaps women can only perform action-mitzvos which are time bound (she'haz'man g'rama), and recite the accompanying berachos. But they cannot recite time-bound berachos that have no action attached. Therefore, they can't say havdalah, nor should they say kiddush levana.
Please refer to the link and their related sources for further explanations.
Rav Nebontzol in his B'Yitzchak Yikareh siman 426:1 he adds another reason why women are exempt from kiddush levana and that is since one is supposed to go outside to recite the bracha then ot would not be befitting since "kol kivudah bas Melech pinimah".
This also appears in Shlomas Chaim Volume 1 Simman 259 by Rav Yosef Chaim Zonnenfeld, and שו"ת אפרקסתא דעניא Simman 22 (both brought by Minchas Asher Shemos 15:2)
The Mishna Brurah notes that although most mitzvos that are a zman grma may be perfromed by women and a bracha can be recited (minhag ashkanaz only), he brings from the Magen Avraham who quotes the Shelagh that kiddush levana is different since women caused the moon to be deficient .