When my daughter was about 14 months old, she came home from day care and announced, "Geegee!" Then she lined up against the wall in the hallway and motioned for my husband and I to do the same. We did. She giggled, moved to the opposite wall and waited for us to move, too. We did. She giggled. This when on for a few minutes, until, we laughingly scooped her up and headed to the dinner table.
Interestingly, when we asked her sitter the next day about the game, the sitter looked at us confused. They had never played such a game. Four years later, we still talk about "Geegee" in our house (which we continued to play every day for months). It amazed us then (and still does) that a toddler could invent a game herself. It clearly had rules: you weren't allowed to stand next to her, you had to wait until she moved first before you switched spots, and it wasn't (happily) over until she was ready for it to be over.
As one-year-olds develop social, verbal, and cognitive skills, they are capable of much more than we could have imagined just a few months ago.
Each phase of toddler development has its amazing milestones. By age two, your child's vocabulary will be exploding, and around three years of age, you'll be delighted by her silly jokes and wish for (occasional) independence.
My advice: take lots of pictures and document those amazing moments. They certainly fly by fast.