My SIL is in med school and she said that if a child favors a particular hand too early (I think under 8 0r 9 mo but I can't remember) they look for developmental problems. Children use both hands interchangably until 10 mo- 1 year then start to develop a preference.
My brother is a lefty as is dh, one of his sisters, and his dad. Dh does most things with his left, but anything he learned from his brother (a righty) he does right handed. His brother (the righty) uses his left for anything he learned from dh. Its neat how it all works
We're curious to see which hand ds favors