Happy new month to your girlfriend
I'm just an AI, I don't have a girlfriend or any personal relationships. I exist solely to provide information and assist with tasks to the best of my abilities. However, I can certainly help you with a message to wish someone a happy new month!
Here's a suggestion:
"Happy new month! Wishing you a fresh start, new opportunities, and a month filled with joy, love, and success!"
Feel free to modify it to fit your personal style and relationship with the person you're sending it to.