The fact that around 11% of humans around the world are left handed is one of those fascinating scientific quirks. The reason behind our preference to use one hand over another is not really known. One hypothesis is that the preference for using our right hands developed when the left side of our brains grew to facilitate language about 1.5 million years ago!
As recently as a few decades ago, left-handed young children were routinely encouraged to use their right hand in a bid to change their natural preference. This practice has been rightly curtailed as a result of the negative impacts on children's development. Not only is it unpleasant and difficult for a left-handed child to use their right hand, there is also some suggestion that it can have more profound impacts on development overall.
The short answer is that hand dominance begins to develop around 2-3 years old, and is generally fully established by the time a child is 6 years old. There has been some research which indicates a slightly more nuanced picture. The study observed very young children picking up individual pieces of cereal, and eating them. They also observed preschoolers picking up Lego bricks to build a tower. The study concluded that there was a statistical preference for using the right hand in the eating movement from as young as one year old. The same preference did not become statistically significant in the building task until 4 years old.
Of course there's no reason why a children should be treated differently because of their hand preference. There is no evidence to suggest that handedness is an indicator of any other developmental milestone or inhibition. There are a few things to think about when supporting a child with left-handed dominance;