Better now than when you've invested two years into a relationship, I tell you that.
If it's such a simple situation, at a month of dating, she's not even your girlfriend.
Nothing to salvage in that relationship at all. Get out now.
If this were a longer relationship, if there were problems or a history of some situations, or if there were enough time to build some trust or whatever, there would be a minimal possibility of working things out if you would really want to.
In this case, get the fuck out of there.