How exciting for you, BrightonGirl! Congratulations on the pg - and am interested in this as I may end up doing the same thing (if I get pg in the next 3m). I, however, have a blood clotting disorder so will DEFINITELY be having the heparin shot.
Go to your GP about it - because you might need to have another one at the halfway stage, and you will need to have a doctor's note or something to get the syringe on board the plane. I always have one before I fly now anyway, even when not pg, but because I'm not pg, I don't bother with the second one. However, if I were pg, I would definitely take the second one as well.
Bear in mind that you will need to have more for the return journey as well - you should be able to get a prescription for 4 heparin syringes. Not sure about Aus but they come preloaded as Clexane (40mg) in the UK - and you are expected to be able to stab yourself. I can't usually - have to get DH or my Dad or someone to do it for me - and if you do get them, I strongly recommend having it in the loose flesh on your tummy (assuming you have any!) as it hurts less there than anywhere muscular.
Whether you go the heparin route or not (and I would recommend it) the flight socks are a MUST, as is the wandering around the plane thing - but since you have a 3yo, I expect that will happen anyway! Certainly did with my 2yo when we went back to the UK in January