I can’t comment on your plans for Uluru but I have just returned from my annal trip to Port Douglas and Cairns.
A few comments about your planned itinerary,
Day 1: Sydney to Cairns
Arrive in AM, take connecting flight to Cairns, chill day, rent car - I would recommend not hiring a car immediately, jet lag and unfamiliar driving conditions can be a lethal combination, also no advantage to having a car at this point. Central Cairns is very walkable and there are lots of accomodation choices near to the action.
Day 2: Cairns
Kuranda Skyrail - there are lots of package options that provide transfers to and from the Skyrail, well worth the money. We like the train + Skyrail option. Kuranda is an interesting village to spend a few hours in and there are plenty of lunch options.
Day 3: Cairns to Port Douglas
Time to pick up a car, there are ongoing roadworks between Cairns and Port Douglas but the traffic flow is well managed. There a great views from the winding road and after Hartley’s, Rex outlook is worth a stop but take extra care when getting back into the traffic, the winding road can make it a bit tricky. Hartley’s is highly recommended, however after visiting the area annually for 15 years we still haven’t found time to visit there but it is on the list!
Day 4-8: PD/GBR
4 Mile Beach - a lovely walk particularly early in the day or in the evenings, there is a netted swimming area at the northern end of the beach, and yes there have been crocodiles from time to time. Must admit we usually swim in the pool at our accomodation and just walk on the beach.
Daintree - a great drive north, easy, frequent ferry trips across the Daintree River. There are also roadworks up here too, cyclone Jasper hit the area pretty hard, but again traffic flow well managed. The Daintree Discovery Centre is very interesting and has a nice cafe, Turtle Rock Cafe at Cape Tribulation is good for lunch and the Daintree Ice Cream Farm has delicious tropical flavoured ice cream on the way back to the ferry. A good one day trip.
Mossman Gorge is also a great day out, interesting visitor centre and beautiful rain forest walks, probably a half day outing
A couple scuba trips to outer reef - lots of choices, tour operators offer good advice about when and where to go, particularly in relation to weather conditions. The underwater scenery is brilliant.
Port Douglas has lots of accomodation choices and plenty of good restaurants. A favourite eating place for us is the Tin Shed, great community group who raise lots of funds for local charities etc, good food and in a stunning location, great spot to watch the tour boats returning to port in the late afternoon.
Day 9 Cairns to Uluru - we usually allow 90 minutes to get to the airport in case of delays and a bit extra time to return the car. On our last few trips we have used East Coast Car Rentals and have been pleased with the service.
Hope that you have great trip.