While it seems it doesn't apply in this specific case, I thought I'd remind everyone that there is also the option of both partners working part-time, so they both have time with the baby while stil keeping their jobs. Obviously doesn't work with every job (or everyone) and if the income discrepancy is too high it might be a hard adjustment, too. But I thought I'd throw it out there, it doesn't have to be one person doing 100% of it, I know several couples who went the half-and-half way and it worked well for them.
To answer the question at hand though, I think, like others, that it's a discussion to have with your wife. If she is to stay home, as seems to be the most realistic option in your case, then how long she stays home will largely depend on how comfortable she is with other people taking care of her child, and how comfortable she is not working.
Since she is a teacher, does it mean the time she takes off would have to be in semester increments?
Also, you say you haven't even talked about a kid... Do you even know that she wants some? It seems to me it's something to discuss early on in a relationship, what if you want some and she doesn't?
About the age thing, in France where I was born and raised, the average age for a first child is 30. Since most people who have children have more than one, it's very common for people to have children at age 35 or more. And France isn't full of people with health issues, so while I'm sure your risks increase after 35, you'd need to look at how much. For instance, I've read that for women, the age they're most fertile is something like 15 or 17, meaning it decreses every year after that. But quite obviously, women in their 20s and 30s are still able to have children, so it's not like 17 is the "limit".
It's just a statistic. Maybe the figure raises from 0.01% to 0.011% or something. I think it's more important for your child that you make sure to be ready financially and emotionally and certainly don't rush due to that clock you think is ticking, know what I mean?
It's certainly good to think about it, though, so you know what to expect. But I think this question is the kind that doesn't havea fit-all answer. Every case is so different that it's really a case-by-case kind of thing, so talking with her and researching what kind of benefits she would get and so on is probably going to be more helpful than asking here.
Good luck, at any rate!