Can my spouse and I agree we have been separated for over a year? In other words, if we agree, does it matter when one of us actually moves out of the house?

No, you cannot “agree” on a separation date. When you file the Complaint you will have to be sworn under oath and sign a verification saying the statements are true to the best of your knowledge so to say you have been separated over one year when that is not the case, is committing perjury before the Court. It truly has to be a year of living in separate physical residences. It also is not enough to move to separate bedrooms but remain in the same home.