I got this in an email from Qantas today. Remember that as an adult you can join for free by signing up to EverydayRewards (BIG W) and then joining Qantas Frequent Flyer that way.
"Get your kids off to a flying start and join them up to the Qantas Frequent Flyer program for free! As members, kids aged from 2 years are eligible to earn points when they fly.
Qantas Frequent Flyer is pleased to offer your kids complimentary membership* to our program, providing you with a saving of $82.50. By completing the following online application form on their behalf, they'll be able to start earning Qantas Frequent Flyer points straight away. You will receive your kid's membership number instantly via email and their personalised membership card will then be sent to you in the post (please allow 14 days for delivery).
This offer is valid from 1 April to 31 May 2012 and only available to children under the age of 18 years who are not already Qantas Frequent Flyer members. If your child is 15 years or above they must join the program of their own accord, as you're not able to action this on their behalf. If your child is already a member and their membership number has been forgotten, please contact the Qantas Frequent Flyer Service Centre on 13 11 31."