As a lefty who couldn't tie her shoes with a bow until a relatively advanced age (6 or 7*), I can give you my own experience with handwriting: started printing at 3, sorted out my backward-K issue at 4, could write my own name in cursive by 5, had to correct a backward-Palmer-Cursive-F issue when we learned cursive in third grade. Is there supposed to be some link between the two activities?
* This may have been a learning-style thing, now that I think about it: I wasn't making progress when shown, but given a set of verbal instructions to follow and repeat to myself, I learned in about an hour.