Yep, you can use Qantas Frequent to book awards on JAL. I have found that I need to research availability online, most reliable being through the British Airways website (you’ll need to join BA Executive Club, but you’ll need a European address - more on this here. ). I assume you can also look at availability through the JAL site too.
Reason for the recommendation is that in booking 3 JAL awards via Qantas, I have often had to call back twice to get someone who can see the availability JAL is offering (and is showing through the BA website).
You won’t be able to redeem your Qantas points for upgrades on JAL, Qantas Points can be used for upgrades on Qantas flights only
To your question on David Jones American Express vs Platinum Edge, Ataraxis is right in that the DJ’s Amex is usually 2x worse off in transfer rates - but Starwood is the anomaly which has the same transfer rate across both cards.
So you’ll earn 0.5 SPG / $ minimum on all spend, or 1.5 SPG / $ on Fuel/Supermarkets with the regular DJ’s card - so yep, better than the Edge and cheaper annual fee. But only worth looking at if you know you’ll redeem for Qantas Points or SPG.
Finally - continue to use JAL or swap to Qantas? I don’t know! Depends on how many JAL Mileage Bank miles you have, how much JAL flying you will do, and how much flying on Qantas you will do. If you’re going to be flying with JAL, I can only imagine it will be more rewarding to stick with Mileage Bank.