You move out and the first thing they're going to do is think that SHE talked you into it. Don't move out while you're on bad terms, I say. Get it settled and to the point where they are not going to be rude and insensitive to her when they see her. Then once you're all talking and it's been accepted, move out then.
What are you going to accomplish by alienating them from the two of you? She might not be your last girlfriend, you're going to want family around should the relationship deteriorate in the future.
Just my 2 cents.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion