Well vagina wouldn't be strictly correct either as that is a specific part. I would find it strange to hear a little one referring to vagina or vulva though. Not really sure why? It just, well, doesn't sound right.
Likewise little boys referring to their penis. Winky, willie etc fine but it just wouldn't sound right to me.
My 5 year old nephew knows the correct term is penis, but he still calls it his 'boaby' which is fine by his parents.
When I was a child my lady bits were known as 'cookie' - I used to be terrified of the Cookie Monster on sesame street 