Port Douglas is a beautiful town but there is also plenty of top places (such as Daintree rainforests, Mossman, Kuranda and Cairns) to discover around the town, so you're likely to look for a rental vehicle. You get to most places by a 2WD car (including the beautiful coastal way between Port Douglas and Cairns), but if you venture further up to the Cape York peninsula, you will need a 4WD. Book in good time and remember that if you get a 2WD, the insurance doesn't cover travelling on unsealed roads!
Courtesy of Tourism Queensland
The major companies you can try to book with are Hertz, Maui, Thrifty, Britz, Apollo, Avis and Europcar. They are large, reliable companies that use new cars that are not likely to get you into trouble, and they also offer one way rentals - handy if you for example want to get to Cairns and use it a a next holiday base.
NOTE: This website is written in British English, which is the English we use in Australia. You will find words like "traveller", "harbour" and "realise", and they are all correct in the language used in Australia.