Hey Mate,
I'm a Cairns local so hopefully I can shed some light.
First of all, what should you target? Up to you really, you can get Jacks, Barra, Bream, Fingermark, Grunter Etc.... from the eustry side of things or if you're lucky enough you can try you luck off Palm Cove for a Mackeral.
As far as where, all really depends on if you have access to a car when you're here. The Marlin Warf (in town) fishes pretty well. Palm Cove Jetty can produce good fish, Barron River Lights Bridge can fish ok too. Also there are some Trawler Loading Warfs around Portsmith that you can fish too.
As far as a rod is concerned, It's really up to you, price up the cost of taking it with you and weigh it up against the cost of a cheapie.
Hopefully that helps.
Now, what class line do you have? Also are you just planning on throwing lures or bait fishing?