Couple things: the JAL itinerary you listed on top was a leisure itinerary whereas the QF flight listed below is a business ticket. And by that I mean those travelling to Japan right now, aside from expats are people who are flying on business. Now if you are a business traveller why would you waste a whole day on a plane to Haneda when you can take a convenient overnight flight on QF to Japan, arriving in Tokyo just before the start of business?
Second, Japan actually has significant competition when it comes to international travel. In particular, they have two major international airlines: All Nippon Airways and Japan Airlines which are on rival airline alliances (Star Alliance vs One World). In addition, there are a number of discount airlines like JetStar Japan and Peach that force the price of international travel down too. Combine that with the connection options in the region like ICN and TPE and it's no surprise that fares from JAL would be lower than QF. Combine that with the fact that travel remains restricted in Japan meaning the only people on those birds, aside from expats will be people connecting through HND to an onward destination. Hence, JAL wants to keep the load factors reasonable so they can secure their route network in the short to medium term.
In general though, it's normal for airline fares to cost significantly more even if they are on the same alliance. That's just the nature of fares. It's supply and demand. Some flights are more full than others and even if you are dealing with the same routing on the same day, there may be other factors at play such as departure time and for those of us who care about status, what airline it is. For instance, pre-COVID I would go out of my way to avoid Qantas or American since I had status with United and they treated me very well indeed as a Premier Gold. Even if the United fare was a little more than the cheaper fare on Delta or American, I'd still pick United for that very reason.
To your point, about when to book flights to Japan, I'm not sure. It's really going to depend on when Japan lifts the restrictions. You may also want to look at other
destinations QF has on sale aside from Japan that may have more competitive airfares such as SYD > SIN or SYD > NAN.
-RooFlyer88