The thing is that kids in general tend to be pushed into stereotypes. This isn't just an unsubstantiated hypothesis I actually remember how adults used do this, for example they don't play with you if you pick up the wrong kind of doll, they don't look at you properly and so on. It's just subtle cues but a child picks them. (every child depends on these cues to learn and develop)
What worries me is that if you continue treating everything with the "over the gender divide" attitude she will get attuned to it, and it will kick off a pretty vicious cycle. So, please do realise that labels are for jars and just let her be, like this awesome dad did for his son.
P.S. - There is this comment http://news.ycombinator.com/item?id=2758516 right above that might answer your quandary in a definite manner
Just wondering: do you now build robots?
Yep. :D
Just saying - girls play chess, too.
There are infinite possibilities for doing things in the world. If not building things, what about the kid who held a speech in front of the UN at age eleven and apparently moved lots of people to tears (don't remember - was it on HN recently?).
You could do some biology stuff, like EO Wilson who went on the trail of fire ants. Some biological drama is probably playing out right now in your backyard.
What I mean is: whatever interests your daughter, there is probably something useful/fun to do.
Well, OK, maybe not that last one.
You know a headline like "My weekend project: father/son NSA hacking" make for a great story to read on HN. ;)
Great book he might want to read: http://www.amazon.com/Hacking-Exposed-Network-Security-Solut...
It seems like our girls turned less "girly" once they started school and of course it helps both my wife and I are engineers. Pink spray paint is always an option...
Build stuff, obviously. Maybe not the same (I for one wouldn't have wanted a checker table as a kid), but building is something everybody should do.
Ask Her.