Yes, girls can get moody while they are on their periods. This condition is called as Pre-Menstrual Syndrome (PMS). Women can be irritable due to cramps, fatigue, breast-tenderness and depression. There are a wide variety of symptoms that they can experience. Some lucky ladies do not have any of them though.
Well, I think it is normal for us girls to feel like that! Imagine bleeding and feeling drained out for at least five days a month. On top of that endure all the symptoms, handle food cravings and un-intended bloating. We have all the right to be moody. You go girl!