It's only been a month. A lot of people have insecurities and anxiety at the start of a relationship. If you have a strong relationship, it should decline with time. To her, I would recommend trying to act and feel more confident until it comes more naturally. To you, I would recommend being sensitive to the fact that she still needs reassurance. When you ask her for something that might make her insecure, try to watch how you word the request. Then do your best to show her that you still care for her. Tell her something positive or give her a hug or a kiss. If you can, see if you can try to do it before she gets to the point of feeling insecure and needing reassurance. When she sees that you're always there for her, she will start to relax and trust you more.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy