Personally, I agree. The process of getting all your legal stuff in place can take time (and you need to do it before cashing in the ticket), so I'd keep working and give notice with enough lead time to allow my boss to back-fill me properly.
Also, with school-age kids, I'd probably wait until the end of the school year to claim, and not even tell the kids until then, so as to not disrupt them mid-year.
Because...
Hey kids! we are moving to New Zealand!