Like I told someone else, there is no set time limit on relationships. It's all about what feels right to you and the other person. Two dates is more than enough to make things more official, though you can avoid looking too needy by just talking with her first. Explaining that you've enjoyed the time you spent together so far and would like to keep seeing where this is going. Girls like feeling as if they are such a hot commodity that you're afraid someone will snatch them away, so just tell her you want a bit more exclusivity because she is far too good of a catch. Or whatever comes to your mind, but let her know you want her and only her if she'll have it that way.
Don't get discouraged if she's not ready yet, though. That doesn't mean she won't ever be. You just have to be patient and make sure you're on the same page. Communication is key!