Atishoo.
If you haven't already found it, try the attached website for a selection of accomodation.
http://www.queenslandholidays.travel...ch_results.php
Hamilton Island has a selection of budget, self catering to 4 and 5 star accomodation. If you'd prefer to speak to someone, you could check availability and offers via the Island Switchboard 00-61-7-4946-9999
Heidelberg is correct, use Jeststar to Hamilton Is (keep your eye open for their regular seat sales) - A Proserpine arrival will require you to make your way to Shute Harbour and an onward ferry to the Islands (which I think is fairly expensive).
Ferry timetables:
http://www.fantasea.com.au/Timetables.htm