Max - I agree that you don't need to tell her specifics. But I'm not sure you should say you're "moving on".
When my W asked me if I was dating, I said that I was in no state to be going out with other women, but I was enjoying making new friends. I was advised that I should have said that while I wasn't in a state to be dating, I was working on myself.
I fear that "moving on" comes across that you don't care for her anymore. And that makes it OK what she's doing.
