I think plane size depends on the time you fly rather than carrier

I would recommend either Virgin or Qantas, NOT Jetstar as it is really cramped
I flew on the weekend and Virgin was more roomy than Qantas
Whichever one gets you to your destination at a reasonable time is the best idea IMO

Many of the car companies do not do rear facing seats but they almost all arrange forward facing so best to ring
When you pack go light on your hand luggage. My first time travelling alone with a baby I took the normal nappy bag and my handbag...the baby is like more hand luggage as you have to carry them too
Now i take a small backpack with everything, it helps if it can fit under the seat in front and an Ergo or some kind of carrier that can be truly handsfree (not a ring sling) is a godsend though they will make you take it off in flight

A bassinette is AWESOME My first experience was with DS at 3 months 2 and a but years after travelling with kids and I didn't know myself
Good luck