Is it normal that i got emotional when i was watching my baby daughter sleeping?

My girlfriend gave birth last week to a gorgeous baby girl and we brought her back to our apartment. But anyway last night i couldn't sleep too well, so i got out of bed and went and just sat with my daughter and watched her sleep. While i was watching her sleep, I suddenly got really emotional and teary eyed just looking at how peaceful she looked, and I suppose in a way i was thinking how happy i am to have her in my life. I'm 21, so is it weird for someone my age to be getting this emotional and are young fathers usually like this. I just seem and feel really silly for getting all emotional like that, because it's not like me lol.