For children under 2, travelling as an infant they don't usually come under your normal baggage allowance. You can take them, port-a-cots etc as additional items.

When traveling with older kids, they do become part of you checked in baggage allowance so I used to plan to send it in lieu of a suitcase for one family member. Although when we travelled last year, the staffer/supervisor at qantas check in told me that she has never charged anyone for a pram for a child under 4. It is their discretion though, and she said most of their supervisors would allow it go the same as an infant.
That's not correct actually. You are entitled to take up to 3 infant/child items per infant/child free with Qantas. That includes prams/strollers, portacots, car seats, etc. Since DD1 arrived, we've always travelled with a car seat, portacot and our pram - a Baby Jogger. Once DD2 arrived, we took an extra car seat for her on top of the other stuff.

We only usually fly Qantas domestically (DH is a Q Club member) and travel a lot. We haven't had a problem with all those baby items flying international either and we've flown with Qantas, Malaysian and Firefly with our girls. We also did a quick flight with Virgin and Sky West with DD1 and again, no problems.

Infants (under 2) don't get luggage (ie a suitcase) until they're 2 though. Some airlines may have different rules so always double check but Qantas is brilliant with kid related items. The big thing to watch is airfares where you're allowed Carry On luggage only. It can cost a lot extra to pay for checked in baggage on those fares and no doubt baby items would incur a nice little fee.