Yes, I do think you are doing the right thing by taking the month off from any contact. Under the circumstances you both need the opportunity, time and space to figure out what (and who) you want. Continuing to communicate during this time does not accurately demonstrate what it would be like to be without the other person, nor does it really allow you to truly date other people and give them / a relationship with them a chance, because you’re remaining connected to your “broken” relationship. You need to start the process of moving on — something she initiated and has already begun.
A breakup is meant to be just that — a break up. Your girlfriend broke up with you. Let there be no mistake about it. And she’s dating someone new.
In honesty, I have a suspicion that your ex-girlfriend may have met this “new friend” around the time she told you that “she needed to be alone to figure things out”. Which, in honesty, was the appropriate thing for her to do (ie: break up rather than cheat) — for both of you… assuming for a second that my hunch is correct.
That said, you have told her how you feel — the ball is in her court. She asked for the space and time alone, you need to give it to her… and not just for her — but for you. No one wants to be with someone who isn’t sure they want to be with them — let alone wants to be with someone else. And definitely not you!
Frankly, I think you should stick to your guns, cease all communication with her, and start dating other women– immediately.
If she loves you as she says she does, she’ll come back to you and tell you she made a mistake in breaking up with you. Then she’ll make every effort to rekindle / resume the relationship with you. And at that point the choice will be yours. If she doesn’t come back — she wasn’t “the one” for you.
I realize this is painful and upsetting, I’m sorry.