Good question. My daughter just turned 5, she is in kindergarten and she does all of her work with her right hand, but does everything else with her left. In fact when putting on shoes, or picking something out she will say I want the left one first. She has used both hands since she's been able to hold a rattle.
From what I've been told, I was the same way. To this day, I write only with my right and do everything else with my left hand. It's weird, but some people are just wired this way my daughters pedi said so I'm just going with that.
My son on the other hand was a strong right hander from birth. He grabbed everything with his right hand, waved bye-bye with his right, blew kisses with his right, ate with right, etc., I think you know where I'm going, LOL! Anywho, he was a rightie from the start, so I guess it just depends on the kid, some you can tell right away, and then there are those who will keep you guessing, like my stubborn little princess.