Hola Pablo ..... gosh, you are leaving it a bit late. There is not much accommodation left in Cairns itself, or the Northern Beaches, you may get some up on the Tablelands, inland from Cairns - Mareeba etc.
Try to pick a few towns in the eclipse zone and see whether there is accommodation available via the Internet.
Alice Springs will not get the total eclipse, though you may want to visit while you are here, the night skies out there are brilliant.
Good luck.
here are a few links -
http://www.iceinspace.com.au/forum/s...ad.php?t=57113
http://joe-cali.com/eclipses/PLANNIN...ers/index.html
http://www.eclipsecairns.com/
https://www.facebook.com/groups/259999150710223/
http://www.astronomy.org.au/ngn/medi...ctsheet_23.pdf