My dd is 3 1/2 so I would have thought it would be obvious by now whether she is right or left handed, but I'm not sure?
I remember when she learnt to eat with a spoon first she was better with her left hand, but then it seemed to swap and, although she used both, she was more adept with the right.
She starts school next September and is just starting to want to try to write letters and numbers but seems to be equally happy to use her left or right hand. Surely by the time she starts school we need to know whether she is left or right handed and probably now she is learning to write we should be focussing on one or other hand?