I would go directly to the source and ask. I've had many losses in my life, including the death of a child in infancy. In my experience, people want to talk about their loss and their grief, but most people are so afraid of offending or of upsetting them (as if they aren't already upset), that they avoid bringing up the issue. This leaves the grieving person feeling alone and isolated.
You can simply ask her if she would like to talk about it, and if so, ask the question then. Give her some time to think about it and then respect her wishes.
When my daughter died, someone asked me if I would like a sampler with her birthdate, weight, etc. I told her, no, because I wanted to do that myself. But it was the kindest thing anyone said to me during that time. She was not a close friend, only an acquaintance, but she did the right thing.
People will tell us what they need. All we need to do is ask. If they cry, it's really okay. They're doing that anyway, and they are stronger than we think they are.