Thank you for reaching out to us.
We appreciate the sensitive nature of this question, which has many facets: physical, emotional, societal, practical, hashkafic, and halachic.
Our specialty is halachic, though we do not at this point issue individual rulings about the permissibility of single women pursuing sperm donation.
In general halachic discussions of sperm donation, sperm from a Jewish donor is only permitted for use when the identity of the donor is known or listed in a registry, in order to rule out an unwitting future marriage between halachic siblings. Use of sperm from a non-Jewish donor is widely accepted, because Jewish status depends only on the mother.
Additional considerations of single women pursuing sperm donation that have been raised in halachic literature have to do with broader concerns about the nature of Jewish family and whether it is correct to deliberately have children who will not know more about their paternity.
Weighing the different aspects of this decision is best done in conversation. Our Yoetzet Halacha Fertility Counselors are sensitive to a wide range of considerations. You can arrange for a free consultation
here. You might also find it helpful to contact one of the fertility support organizations listed on our site
here.
We hope this helps. Please let us know if we can be of further assistance.