I am not sure how many people really know before their child is 3 - especially if it is their first child.
However, with 20 20 hindsight, I should have known. My son taught himself to read. He learned basic phonics in one day at 25 months. His memory was amazing - remembering books, remembering things that had happened 6 months earlier.... His puzzle working skills were great.
Like your daughter - he would switch gears. He would say a word - and then you wouldn't hear that word again for months. He could sing a song and carry a tune at 15 months. You couldn't understand a word - but he had the notes and rhythm right.
Even so - I didn't suspect that he was that special until he was turned down for admission to preschool at age 4. The school said he was too academically advanced for preschool and not mature enough for 2nd or 3rd grade. (Their estimate of what it would take to keep him challenged.)
Check out Ruf's Levels of gifted online as a quicky starting point. It isn't perfect - but it is accurate enough to give you an idea of how much more you need to learn about giftedness.
Knowledge is power....
Where have I heard that before?
