Is this normal for a 9 month old baby?

yes this is so normal. It means your baby is smart, and is telling you she wants a particu lar item or wants to be up. she's developing a preferance.And feels safe to express herself. just redirect her when she wants what she can't have, and reure her at nap time and check on her, but she will learn nap time is nap time if you don't get her up.