Hi there,
We took our Joolz pram (pretty much the same size as a bugaboo) back to oz with us last year in a Stokke pram bag which you can check-in as oversize luggage at no extra cost. It can also fit some small toys, nappies and a blanket inside too which helps. The pram arrived safely without any damage. But to be honest, we haven't used it since then as it's been a bit easier to travel with a fold up Maclaren pram and we are not bothered if it gets thrown around. It's much easier to pack in the boot of a hire car too. We just walk it straight to the gate and leave it at the plane doorway for the staff to store below. It hasn't been marked or damaged and we've traveled quite a bit!
All the best with your baby and enjoy the nice weather back in Australia. We'll be going again in March and really looking forward to it.