Or the more frequently used, but far less elegant: "Girls flake"
I could very well mean that as I only ever use the expression in spoken language .
I always figured it was French. La donne (the lady) est (is) mobile (changeable). French classes have been a while ago but I can't recall the meaning of è.
Also, "donne" doesn't mean anything related to women and "mobile" rather means something like "movable" in French
You seem to be correct, it's Italian. Further "donne" is present as "dame" in the French language so I figured it was 'old French or something and I imagine 'movable' meaning 'changeable' in a language is pretty common.
Anyway it's a nice phrase to utter when a female friend is being inconsistent (which occurs often )