what is the Australian nickname for Chris?

Chris is already short for the likes of Christopher, Christian, Christine etc Might get Chrisso, but Chris is really common.

Alex is in the same boot (being short for Alexander or Alexandra). Alex is pretty common. Either are more likely to be shortened to Lexi or Xander or Ally or something...

Never heard Carol shortened (though I have Caroline shortened to Carol or Caz or Cazza)

I know two Christophers who answer to Kit. That is not particularly Australian. The British playwright Christopher Marlowe (1564 - 1593) was known as Kit Marlowe and in America, a famed trapper, guide and scout whose name was Christopher was known as Kit Carson (1809 - 1868).

Alex is one of the abbreviations of Alexander. Others are Al, Alec, Xander and Sandy. Carol has no common abbreviations or nicknames that I know of.

Not all names have nicknames here. Chris might become Christo, Alex Al, Carol Cazza.

TH, no, Chris is the shortened version of Christina, Christopher. Alex is the short version for Alexandria or Alexander, Rob or Bob is shortened for Robert.

No nicknames to really be had.

Chris is usually a nickname already.