Some comments, which will hopefully be of some use:

Great Ocean Road

This is one of my favourite places in the world, both from a driving perspective and also from an amazing scenery perspective (it is one of the greatest driving roads in Australia, if not the world), so definitely worth a visit, especially if you plan on coming back at a later date and exploring Melbourne.

Uluru

The rock is only open to climb approx. 100 days a year and is closed at 8 am if the forecast temperature for the day is above 35 degrees centigrade (probably not a problem in October) or if it's raining or too windy. The local Aboriginals request that you do not climb it at all. The base walk takes about 2-3 hours and is worth doing. Sunrise and sunset at the rock are must do's. It might be worth doing the dining under the stars - it's expensive, but I suspect it would be a once in a lifetime experience.

Sydney

If you like nature and bush walking, I believe the Royal National Park is worth a visit - it's one of the oldest National Parks in Australia , if not the world, and it's very close to Sydney (I think you can catch a train that will get you there), or it's a short drive in a hire car. I haven't been there, but it's high on my list of places to visit.

Blue Mountains are also worth a visit, especially if you like nature and bush walking. One of the best walks is the National Pass (search for it on google), which takes a few hours, but is spectacular.

A trip to the Hunter Valley is worthwhile if you like wine.

Given your limited time, a hire car would be required for either Hunter or Blue Mountains.

Melbourne

Dinner on the tramcar restaurant is worth considering - very unique and very Melbourne. It's dinner on an historic tram (circa 1920's), many examples of which still ran in Melbourne until a couple of years ago. Food is supposed to be good (but not top notch, given the limited space), but it's expensive.

Port Douglas

Sheraton is not that close to the main street of Port Douglas, where all the restaurants are. There is a shuttle bus that operates from Sheraton to the main street, but not sure of the frequency or operating hours. Sheraton is also expensive for what it is - I understand it's a bit tired, being not that new.
There are options which are cheaper and closer to the main street.

Domestic Flights

If you haven't already purchased your flights, Virgin Australia offer discounted flights to foreigners, via an 'Airpass'. Flights start at AUD 79 for short distances. To be honest, you can often get cheaper flights than this, but it's worth considering.

Car Hire

Not sure what country you are from (but assume you may be from the US given you have quoted many things in USD) or whether you know much about car hire in Australia, so here is a brief overview:

Car hire in Australia always includes, as part of the rate, insurance for damage to the rental car, other cars and other property, plus legal liability for injury to other persons. As far as I understand, this is a legislative requirement. The coverage amounts vary from state to state, but are generally very generous in comparison to the US. Note that the included coverage cannot be declined.

The catch is that there is a large excess/deductible payable in the event that the rental car is damaged. This amount varies from a min. AUD 2,750 to over AUD 10,000 if the car is rented from an off airport location, depending on which state, type of car, which company the car is rented from and whether another car is involved. These amounts increase by a few percent to over 20% if the car is rented from an airport (% varies depending on airport).

The cost to reduce this excess to either zero or a few hundred dollars is approx. AUD25-50 per day, depending on the car, company and where the car is hired from.

Most rental car companies provide no cover if you drive on unsealed roads.

No cover is provided for underbody, roof or water damage. Driving at night in remote areas is often prohibited.

Most overseas issued credit cards which provide travel insurance and/or rental car insurance, specifically exclude cover for rental cars in Australia (there are some non Australian issued cards that do cover rental car excess in Australia).

Travel insurance may provide rental car excess cover.

For example, I checked car hire for a US resident from Ayers Rock Airport for one day from Oct 9 and this is what I found:

Hertz:
Cheapest car - RAV 4 - AUD 74.18
Km - 100 included then AUD 0.25 plus taxes and charges per km
Excess - Accident Damage Excess (ADE) AUD 3,894 + Single Vehicle Accident Excess (SVA) of AUD2,596 if no other car involved (e.g. you hit a kangaroo), for a total of AUD 6,490!
Excess Reduction: approx. AUD 33 per day to reduce ADE to approx. AUD 500. Note it appears excess cannot be reduced to zero and SVA cannot be reduced at all.

Avis:
Cheapest car - Hyundai Getz 3 door manual - AUD 168.60
Km - 100 included then AUD0.336 per km
Excess - Accident Damage Excess (ADE) AUD 3,440. No additional SVA.
Excess Reduction: approx. AUD 31 per day to reduce ADE to approx. AUD 400. Note excess cannot be reduced to zero.

Budget: not available

Europcar: not available

Thrifty:
Cheapest car - Hyundai Getz 3 door Auto - AUD 80
Km - 100 included then AUD0.28 plus taxes and charges per km
Excess - Accident Damage Excess (ADE) AUD 3,894 + Single Vehicle Accident Excess (SVA) of AUD2,596 if no other car involved (e.g. you hit a kangaroo), for a total of AUD 6,490!
Excess Reduction: approx. AUD 27-33 per day plus taxes and charges to reduce ADE to approx. AUD 500 or zero. Note it appears SVA cannot be reduced at all.

As you can see, your AUD 50 for a day may be a little unrealistic.

Expect to pay AUD 1.50-1.80 per litre for fuel there as well.

Happy to answer any questions.