It terms of language/walking your DD sounds similar to my DD. She walked at 10 months, after hardly crawling at all. And she spoke early too, and was using sentences at 18 months. She tsill talks non stop - at least now it is aimed at her dolls, Happy Land characters and some imaginery friend we seem to have staying with us at times right now.
I still do have to play with her at times (either voluntary or at her insistance), but the latter is much less nowadays. She loves me to play with her, but if I can't for some reason (cooking, working, etc.) she will normally play on her own happily. Certainly her ability to accept that bit has developed a lot in the last couple of months or so.
As I mentioned before - not sure why some children play on their own and some don't. I personallythink it is just personality, rather than related to learning/development maybe.