You might look at getting a folding stroller. With our Quinny Zapp we've done 25 sectors (to/from UK three times on BA plus around Europe/Asia) and never had a problem putting in o/head locker on B737/B747/B747. Check in staff usually tag stroller in case of gate problems but we always fold & put in carry bag at gate and board early (as with a toddler) to ensure empty lockers, and no-one has ever queried. This has proved very useful on transits - even doubles as a bed when you're seated in the lounge if you tilt back & hold handles on your lap. We bought ours in UK - as ever, you'll get ripped off in Oz but there's always the online auction sites!