Welcome to MDC!! You'll find this site a great resource and hopefully some more women that have undergone a unilateral oophorectomy will jump in and share their experiences. I might suggest cross posting over in the infertility and trying to conceive forums to see if there are any women there with success stories.
I am no expert whatsoever, but it was my understanding that the one ovary would produce eggs every other month, but perhaps this is only in some cases and in others the one ovary will take over? I'd have to do some more research to find out! I did find one study (below) that compared women with 2 ovaries to women with 1 ovary during IVF. They found that while the women with only one ovary produced less follicles, oocytes, and embryos, but the fertilization and pregnancy rates were the same. I would conclude from this that the eggs that were produced by women with one ovary were of no lower quality and the women were no less able to sustain the pregnancy than those with 2 ovaries.
Women with one ovary have decreased response to GnRHa/HMG ovulation induction protocol in IVF but the same pregnancy rate as women with two ovaries
Lass, A., Paul, M., Margara, R., Winston, R.M.L.
Inst. of Obstetrics and Gynaecology, Royal Postgraduate Medical School, Hammersmith Hospital, Du Cane Road, London W12 OHS, United Kingdom
The study compares the response after gonadotrophin-releasing hormone agonist (GnRHa) and human menopausal gonadotrophin (HMG) stimulation for in-vitro fertilization (IVF) in patients with either one or two ovaries. The study group (group A) included 73 cycles in women who had unilateral oophorectomy before their IVF treatment and the control group (group B) included 988 cycles in women with two ovaries. Tubal disease was the sole cause for infertility in all cases. The two groups were similar in age and parity, The patients with one ovary required more ampoules of HMG (62.9 versus 48.9, P < 0.001), a longer induction period (13.5 versus 12.7, P < 0.01) and had significantly lower oestradiol concentrations on the day of human chorionic gonadotrophin (HCG) administration (5840 versus 6473 pmol/l, P = 0.035). They yielded fewer follicles (11.2 versus 13.1, P = 0.005), fewer oocytes (7.3 versus 9.1, P = 0.006) and produced fewer embryos (4.4 versus 5.1, P < 0.05). There was no difference in fertilization rate (60 compared with 58%), or pregnancy rate (25.8 compared with 27.1% per oocyte retrieval). Women with only one ovary responded less well to GnRH agonist/HMG stimulation than women who had both ovaries but pregnancy outcome was the same in both groups.