I do think this is interesting, even though I can see it's a question with a lot of tensions bound up in it. I certainly agree that there are problems with associating educational level or types of job with intelligence. I'm educated but not super-super intelligent.
But, if we're going with educational level, my mum and I both have doctorates and we talk about this quite a lot. I think (and she thinks) that small children are really intellectually fascinating. I can see how if you're not particularly interested in analysing people/thought processes, you might get bored with a toddler. OTOH, I think it's very absorbing parenting if you're able to engage on lots of different levels, thinking about what the child's doing and being really interested in how they do it.
I don't buy that intelligence has anything to do with rationalising emotion, thought. I have known some scarily intelligent people whose emotional reasoning was shite. And I don't see the issue, either. Personally, I am delighted to have a toddler and hugely enjoy the whole-hearted way she doesn't judge and does love me - though I am also well aware I stand somewhere below teddy, Assan from nursery, and next door's cat, in the pecking order.
I really do think a big issue is simply social pressure, which I don't think acts according to intelligence, but according to class bias. I've always wanted kids; DP didn't want them until quite recently. But I'm middle-class and went to university, and so until my mid-to-late 20s, people were constantly telling me anxiously I was far too young to think about children and pressuring me not to have them. Having kids aged below about 22 would have been seen as really a 'failure'. By contrast, DP was expected to have children. 16 would have been seen as worryingly young, but 20 would have been perfectly respectable, and by the time she was 23 or 24, it was semi-expected. By the time she was 35 and pregnant, some people considered that almost indecent.
We are both fairly intelligent women, both degree educated, and both worked in similar jobs until recently. The big difference is the attitudes of people to a 'working class' girl from a council house, and a 'middle class' girl who wasn't. Anyone who thinks those attitudes don't follow you well into adulthood is kidding themselves.