lisa,
Best time to see the reef is now!!! Visibility has been the best its been in months, with a very mild monsoon. May, and early June for the last few years has been relatively quiet in and around Cairns and Port Douglas, the peak tourist season starting in July.
Water temp has been around 23C, visibility up to 40m and the stinger and Jelly fish problems that plague the coast over the monsoon is dropping considerrably. Most of the dive boats have seasonal introductory prices, two for one deals and extras to kick them off for the coming season,as they are normally startig with new crews. Other options are to work as a "hosty", which some of the "floating hotel" boats do to lower there overheads, and you get free diving and accommodation, and food for u working on the boat in return...these positions normally run for four to five days. and the crew are experienced and alot of fun. As far as i know work permits are not needed....but shhhhh....don't let it get around. If u want to avoid the crowds, don't even go near the reef from late june - october....every man and his dog is out there.
hope thats some help to u
Davo