My son started off remembering coinciding days, but turned into ... by the time he was five. He used to put all his teddies' "birthdays" into my phone and just remembered everything

Memory is a tricky thing. It is hard to distinguish an eidetic memory and an awesome one. I used to have a great memory, and I was like your DD in not having to study for a test and just remembering the answers. Since having children, I now have a terrible short term memory, but still a good long term one.