Quoting l☮j:" Would it be a bad idea to start applying for jobs now, if we're not moving til April 21st? Or should I just wait til we actually get moved and settled in?"
I'd wait until at leats a little closer. The reason is that if it's too far away, even if they call for an interview you won't be able to go, so they won't choose you, you know? If it's close enough to go to interviews though then it's fine. Just tell them when your start day would have to be,.