R.S.
Since you say your supervisor is aware that you will eventually take another job, it may not be a bad idea to say that you are looking at other positions at this time, as an FYI -- as long as you keep the mood positive.
"I love this job, but unfortunately living in NY is getting too expensive for us, and so my husband and I really have to start making plans to move out of state. So I just wanted to let you know that I am looking at other positions right now (in Fla or don't mention that if you don't want to)."
I think it will help to keep her updated as frequently as possible -- so the minute you get a position that you feel strongly will be "the one," you can tell her at that time and then quickly remind her that you will be available, even after you are gone, to "train" the new guy - and then you can leave behind your contact information the the new person to contact you and ask questions. Even if you are not that available to help out with "training", I think it's professional at least to offer some assistance, so your mentor does not feel excessively burdened with training a new employee.
As an addendum, I just read the other responses, but IMO, in your profession, I don't think this is the best way to go (I work in a similar field). I understand waiting until you get an offer, but you already know that you are leaving NY for sure, and pretty quickly, right (like in the next 6-8 months)? If that is true, then I see no need to wait until you get an offer, since you want to minimize an abrupt leave as much as possible. Especially if you are a child psychologist, that means you much have patients or some other form of continuity in patient care, and with chldren. You want to minimize any discomfort to both your employees and to your pediatric patients as much as possible, I think. So, two weeks notice is not enough time to make a successful transition, IMO. I left my first job -- actually, I too left NY to move to a cheaper location, and I told my employer of my plans a few months in advance, even before I interviewed, since I knew for sure we were leaving NY in the next 6-8 months, whether I was employed to not (my husband would support me) -- therefore, the office had time to transition patients to another physician and I was also able to tell some of my old patients good-bye.
