Going from a food style page to a baby niche might be a hard sell for the friends that you have already. You could put out a poll on the current Facebook and ask what the people would say about it. Never can hurt to ask there as well. Maybe someone will have a better idea of this either way I hope this helps you.
All the best.
Douglas

If you want to use the same Facebook page for your current website in baby niche, you would still have your followers. But if you make a new page, you might loose track of your followers. You might want to use your old Facebook page and link it to your new Facebook page if allowed. just something to think about. Good luck!