In that case, I'd see if you can fly to Cairns as soon as you get to Brisbane. http://www.webjet.com.au will give you a list of all the possible flight times and prices from Brisbane to Cairns on a particular day. It is actually about $10 cheaper to book with the airline direct, so after you've found a suitable flight, book with http://www.virginblue.com.au, http://www.qantas.com.au or http://www.jetstar.com.au
Virgin Blue are the best for the short routes, I've found.
After spending two nights in Cairns, you won't have much time left for Brisbane, but there are a few things you can do. There are day trips to Moreton Island, Australia Zoo, the Sunshine and Gold Coasts or you can stay in Brisbane and tour the city. Check out the Southbank Parklands, Kangaroo Point Cliffs and Roma Street Parklands - all are fabulous places for a stroll. Also check out georgiamorrison's post on things to do in Brisbane - there's tons of great info there.