Is it In accordance with the code of Jewish law for an unmarried 37 year old Jewish woman to go through the procedure of having her eggs frozen?
First of all, I want to give her a Brocha that she find her Bashert very soon so this answer will only have to be theoretical.
There is room according to Halacha to be lenient, in very specific conditions, when it is done under the supervision of a competent Hashgasha.
In regards to Hashkafa whether using such intervention is appropriate, there are many factors to weigh in: on the one hand once a person reaches the age of 35 the possibility of one being able to get pregnant in the natural way slowly decreases.
However, on the other hand, there are many Chabad Rabbonim that disapprove of such intervention and their view has support from various answers from the Rebbe on this topic. Also, there is always the possibility that her future husband may not agree to such procedure (the desire to have children the natural way is self understood and is based on strong ethical and Haskafash considerations), and therefore this route may not be the preferred one for her in this situation.
One should also weigh the fact that the success chances of such a procedure decreases significantly after the age of 35 as well as the regular potential side effects and risks and prohibitive price. The risks, though rare, include intra-abdominal bleeding, abscess, ovarian torsion, etc. (Aragona, C., Mohamed, M.A., Epinola, M.S.B. et al. (2011). Clinical complications after transvaginal oocyte retrieval in 7,098 IVF cycles. Fertil. Steril. 95:293-294.)
The American Society for Reproductive Medicine published a paper in 2007 that labeled egg- freezing as an “experimental procedure” and “not an established medical treatment” (ASRM Practice Committee. (2007). Essential elements of informed consent for elective oocyte cryopreservation: a practice committee opinion. Fertil. Steril. 88:1495-1496.) The primary concern is the safety of the fetus created from thawed eggs, though studies have not shown any negative outcomes in children born from thawed eggs (Chian, R.C., Huang, J.Y.J., Tan. S.L. et al. (2008) Obstetric and perinatal outcome in 200 infants conceived from vitrified oocytes. Reprod. Biomed. Online, 16:608-610. Credits for the research material to C Kaufman, Derech Hatevah, 20, p. 27). Of course, there are arguments within Halacha – aside for Hashkafah – about the permissibility of undergoing an elective surgical procedure involving also general anesthesia, though as mentioned there are strong grounds for leniency. (See a similar discussion here, though the issues are considerably different).
Therefore, I would strongly advise you to speak to a local Rav who knows you and discuss with him all the pros and cons of such an arrangement. Iyh we should hear Besuros Tovois very soon.
Clarification: The opinion of Chabad Rabbonim on the matter of IVF is far from unanimous, with many being of the view – which is corroborated by many written and oral sources – that the Rebbe was strongly opposed. This response is not be construed as taking a position on this matter.