I have no idea about the pregnancy progressing normally from here. I would think so, since the ovaries already did their part. But that would definitely be a question for the doctors.
As far as concieving with one ovary- your ovaries take turns each month releasing an egg. So to only have one functioning ovary means she will only be fertile every other month. I'm not sure if you can know which ovary's "turn" it is, to know whether you will be fertile this month or not. But it is definitely possible to still conceive with only one. It will be more difficult and likely take longer since she is only fertile half the time as someone with 2, but still possible. Lots of women only have one functioning ovary. She should see a fertility specialist when she is ready to try to get pregnant again, and they can most likely do all sorts of things to increase her odds of getting pregnant.
What a scary thing. I'm so glad the baby came through the surgery.
Edit to add:
Laurie could be totally right on this, I'm not sure. I was repeating what my cousin's doctor told her who has had an ovary removed. Guess the best thing to do is have her ask her doctor.