L.L.
My first child was like that...so independent. But one day I just sat down and started playing with her, even though she didn't ask...and she was overjoyed. I was so surprised...it wasn't that she didn't want or need me to play with her...she just was such a good girl, she didn't ask.
It's really a blessing with a child like this, believe me...you can sit down each day and spend some quality play time, but at the same time you can get your housework done because she'll entertain herself. Even if you're not sitting with her, you can talk to her while you're getting things done.