It is normal to date for a long time before becoming in a serious relationship?

I am with this girl that is about three years older than me and she does not want me to label her as my girlfriend as yet but she just wants to date me. We kissed once, but when I brought up the topic of labeling her as my girlfriend she told me that she was not ready and that we should just keep things as they are until she makes up her mind….should I continue seeing this girl with the hopes that she becomes my girlfriend, or is it alright for me to date other girls and find one that wants me to be labelled as my girlfriend?