Colostrum & Second Baby?

My husband & I currently trying to get pregnant with our second child. Our first is 6 months old. I plan to be feeding him still by the time our second child is born. Since I will already be producing milk, does that mean I won't make colostrum? Will my second child miss out on that nutrient & antibody rich pre-milk? And if I do make colostrum, will my first get it too? This probably seems like a stupid question, but I'm just confused by the idea.