Can give a few more data points on this, Mrs eastwest101 + kids had to apply for an exemption to travel from Australia to Japan (direct NH flights still operating SYD-HND) due to an urgent family medical emergency of a relative in Japan.
The Dept of Home Affairs Travel Restriction Exemption site is a little misleading, because it asks for your intended flight dates and flight numbers, sending us scurrying away to book flights, as approval can take anywhere from 4 weeks to 3 months which is obviously a ridiculous time frame for medical emergencies.
So we got the flights booked and Doctors letter together (which thankfully was already in english) and did the application, and sure enough the first auto-receipt email from Dept of Home Affairs upon lodging said not to book flights (
facepalm), but to await approval. As it turns out - our particular situation was approved within 24 hours to their credit. So then thankfully NH have played reasonably nice and we have been able to bring SYD-HND flights forward to something much sooner as all incoming pax into Japan have to serve a 14 day quarantine, so its still a gamble as to whether they will make it in time anyway.