Would be a busy trip. The time and cost to get the destinations (fly/drive) will take a reasonable amount. With time to airport, hotel check-in, etc many will take the best part of a day. Some places will have limited air schedules. For AYQ may need to go via ASP as well.
Have you priced out cars, air fares & accommodation?
Great Circle Mapper
https://en.wikipedia.org/wiki/Ayers_Rock_Airport
https://en.wikipedia.org/wiki/Alice_Springs_Airport
Why both Fraser Island and Lady Elliot Island? I would suggest 1 only of these Queensland islands.
https://en.wikipedia.org/wiki/Lady_Elliot_Island
SYD may give the best city experience, provided you stay within 0.5 mile of water. BNE the worst.
November is a good time to travel.