Given that the travel date is fairly close (for award travel), I would try and get the flights booked within the next few weeks. You should be able to manage a transfer from AMEX to SPG then to a third program well within that timeframe but you'll want to research availability before you commit to the transfer. There are several ways to research availability, one which is to sign up to the frequent flyer programs as I previously suggested or alternatives like Awardnexus.
Dont forget about airline partnerships - a prime example I can think of is Qatar airways which I understand flies from Perth to Doha, which is very close to Dubai. While they are not part of oneworld yet, once they join, you'll be able to transfer your miles to either cathay or Malaysia from amex and book a flight on Qatar airways. This isn't something I can recommend for your particular trip however, since Qatar isn't oneworld yet and your travel dates are fairly close.
There's obviously nothing stopping you from transferring your points to SPG then into Qatar or any of their current partner airlines (such as ANA) which will let you book their flights as of today. Obviously, similar arrangements are available for Emirates with their partner airlines so this is something you can research in detail if you feel its worth it.
With your krisflyer question, the wait list means the seat won't be confirmed when you make the request. As it says, you go on a 'wait list' and if a seat becomes available, you can choose to go ahead and ticket. SQ generally are fairly decent at clearing wait lists but it can be a complete lottery especially without status and it may not even clear at all so you want to have a backup.
As for transferring your MR to QFF, the only way you will be able to transfer your existing MR points to QFF is if you sign up to the amex platinum charge card. This is because when you sign up to the platinum charge card, your MR account will be 'converted' to a ascent premium MR account which allows for the transfer. Simply signing up to a qantas card means while you'll be able to earn on your new spending a which will go to QFF, your existing benefits will sit with your current MR account which won't be transferable to QFF.