We flew to Sydney Feb last year with Steph. She sat on the Man's lap, so can't really help you with that aspect, but the wrapping up in a sling sounds like a good idea.
I'm not sure that I would trust airlines or others like that with a baby seat. We didn't even take the comfy pram for her, just the cheapy stroller, which got bent anyway!
We hired a car through Hertz, with a baby seat, and they were happy for us to check the seat that we were happy with it and how it was fitted.
I can't remember what the allowance was for Steph in terms of baggage, but there was more than enough allowance for all of us even with the stroller. Hope that helps.
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