I started a PhD start of October - and it quickly became apparent that the department I'm working with is very chaotic. Now, almost 5 months after I have no project, no research plan or whenever I try to talk to my supervisor she says there's plenty of time and we'll see what happens, because she is applying for some funding at the minute. A post doc quit recently so now, I am mostly doing and continuing his work, which is fun but not a 3-year project. My supervisor is quite nice but very dismissive and laid back. She oversees 4 PhDs and 2 Postdocs as well as some masters and undergraduate students which I thought was a lot?
I have applied for another PhD, starting in October next year as I don't want to be left with no options if in couple of months it all goes bad. Now, I got accepted for the new PhD and it is a very good project and I might want to take it.
My issue is I don't know when to tell her? I hope she will be understanding, but if she's not can she kick me out before the end of this academic year? I don't want to tell her a month before I go but I don't want to be stuck for 6 months as I need to live off something before the other one starts.

Thank you!