What makes a dog person?

The dog is taking ques from her body language. Think about the info we get from watching a dog and think about how it effects us around the dog. Same thing just from a different perspective. If we she an unsure, skiddish dog we approach with caution, guarded, just like you described above. You had apprehensions about the dog, (just as a dog will do with us if we look uncertain) your daughter is probably too young to have these instincts in her yet, so she just walks up to the dog with none of the mental baggage that you or your older daughter would bring. Its that expectation that makes the dog "peculiar".