We did - from memory it was 2 "baby items" - ie cot, car seat, stroller - for free.
You check them in at the airport at the oversize baggage counter, the checking girl will give put stickers on them for you and most airports have cheapie umbrella strollers to use to the gate, i usually use the Ergo or just carry her though.

I hate to say it, but I think your mum is right lol I wasnt going to take my pram to Melbourne not long after Charlotte was born, but mum insisted and I would have been so frustrated without it!

Have a good trip!