It will go as oversized baggage with Virgin and JetStar, with Qantas they will take it at the check in desk with your other bags.
We travel with ours all the time and never had an issue, it will come out on the conveyor at most airports.

Check with your carrier, but the ticket you buy with and infant usually has an allowance for some sort of baby luggage, like prams and car seats.

HTH