Sorry Dunerider,
I have no kids and I am single and also I am overseas at the moment. But I am originally from Brissy and have been back a number of times and I have lived in Sydney,Melbourne Darwin and Brisbane. Brisbane would have to be the cheapest.
Fuel has allways been cheaper at the pumps than Mel, or Syd sometimes 10 cents/litre cheaper
Groceries I found are much cheaper Brisbane than Darwin , and Sydney.
Prolly Melbourne and Brisbane seem to be the same but one is definitely warmer
Try this site it has a world ranking of cities has data on Australian Cities
Hope theseis help.
http://www.abc.net.au/worldtoday/s599514.htm
http://www.finfacts.com/costofliving.htm
Regards
Sheep
p.s. did a google search, it may give you more info.