The only way to “purchase” JAL miles is through purchasing SPG points and convert to JAL miles. They are having a sale at present at 25% discount so it’s the best time to buy. Please note each account can only purchase a maximum of 20000 points per year, so you need to register 4 family members, and purchase 20000 miles each and transfer to your SPG account. But note that you get bonus 5000 points each time you transfer 20000.
But you can also purchase AA miles. When you use AA miles, you don’t look at JAL’s award chart, but on AA’s award chart. Currently it’s 45k one way to Japan. So I would advice you to wait until Mar 22 next year as AA will “devalue” their chart and AUS to Japan becomes 40k one way, or 80k return.
AA search engine doesn’t show JAL award space. To find it, you need to check it with JAL’s own website or through BA’s website. Both require you to have membership. It’s free to join, except for BA you’ll need a non Australian address (just use your friends or relatives overseas). If you can see award space on those 2 sites, you can call AA and book them.
You can use Qantas points, Asia miles points, or any one world currency to book JAL seat if available, but each program has different award chart and will cost differently.
Hope that helps.