On the other hand, she is certainly different from (say) what she's likely to be in 15 years' time, in ways that are clearly related to her age. There are things I wouldn't say or do with her because they aren't "age-appropriate", though I wouldn't use that particular term. If someone who didn't know my daughter tried to tell me that I couldn't do this, that, or the other because it wasn't "age-appropriate" then I might react in roughly the way jdietrich did; but if my wife did, then I hope I'd give her the benefit of the doubt and assume she meant "appropriate for who and what she currently is". (Though I might have trouble giving her the benefit of the doubt in a situation like the one in the original article...)
As for the original situation, I don't think there's any point trying to pass judgement on what they said to each other in those first few minutes. No one is at their best in that kind of situation. On the face of it, at least, what they ended up doing seems to have worked out well enough for them, but of course it's quite possible that we're hearing a distorted version of the story.
Exposure to phenomena like "kids" is rather abundant in most societies. For parents as well as non-parents. Observation and analysis about how those phenomena processes seem to be behave can even sometimes be made more accurate by those not emotionally bound up in the here and now.
I believe there is no argumentative authority arising from the fact that one is or is not a parent.
To settle what might be an authority issue for you: I don't know about jdietrich, but I have kids and I mostly agree with him.
I am not a parent, and I had a good enough childhood (though I think I could have been given better schooling), but I have a four year old niece and she definitely is a person with her own worldview and her own feelings. I can have a conversation with her as I can with somebody else, regardless of age.
If you take people seriously, no matter what they look like, I promise you that you will have a richer life.