It is a normal feeling to have,
but..
You've been going out for a month, haven't had sex and I assume you're not an idiot and will use a condom. A reasonable question to ask might be to find out whether she has had an STD or whatever, touchy subject I know but necessary before you have sex for the first time. But there isn't really any good reason to delve into her private life otherwise, is there?
It strikes me that if she does tell you, she'll tell you something you don't really want to know. Suppose she said 'well actually I shagged X at my college'. It would just make you paranoid.
I say you just have to trust her. Asking questions on her private life will just make her feel cramped and pressured. Try and be cool with it, the fact you know she isn't a virgin suggests the subject has come up and she hasn't gone into any more details, so why get her to go into it more? She is with you now, see where the relationship goes without bringing your insecurities into it.
If you're interested, the reason I feel this way is because I too wanted to know about my gfs past private life, and this just made her feel untrusted and pressured, and when she did eventually tell me, it was something I didn't really want to know. So I learnt my lesson.