To the OP:
Inside Cairns itself, there is nothing that qualifies as a luxury hotel. You will need to go outside of Cairns - a few suggestions have already come through from others.
Westin Sydney is not a luxury hotel. It's nice enough but not 'luxury' per se, so if you go there expecting a luxury hotel, you will be disappointed. However, if you call most 4/5* hotels 'luxury', then you'll find it to be OK.