My son could also do math in his head at preschool age and like your daughter, seemed to have a large capacity for information. He liked a book that I think was called "The Big Book of Tell Me Why" and it had so much interesting information that I didn't even know and it was around that time that I thought he sounded like a "little professor" because he used big words and loved to share his knowledge with other people.
I really enjoyed my son at that age. I wrote a lot of things down that he said at that age and I still like to look at those notes sometimes. It brings back pleasant memories.
