Hey Tomo,
Congrats mate. It's good to see I'm not alone. We had our first 5 weeks ago.
I remember there was a writeup in Australian Flying May-June 2015 about flying with children. Apparently a car baby seat is legal to use in an aircraft, if it is compliant with Australian standards AS/NZS 1754. There is info in CAAP 235-2
Biggest issue I can see is how to fit the top strap. The car has those mount points in the back, but I wouldn't think that the tie down points in the rear of a plane would be suitable.
I think as to age, it would depend on the baby. For me I'll wait till the 12 month mark. I also want to take him in the kid trailer behind my push bike and the advise is 12 months onwards as they can hold their heads up and deal with the bumps. Once I know he's ok in the trailer, I'll try the plane.
The other things the article mentioned were hydration, ear protection and dealing with changes in pressure. With the pressure issue, baby should be ok, unless they have a cold/ear infection. To deal with popping ears, the suggestions I've had are to use bottle or pacifier during altitude changes. That way they have something to suck/chew (Similar to an adult chewing gum.)
Anyway, hope this helps.