Hi emsec and welcome to TT,
The description by jingili of how the weather will be for you is much as you can expect and certainly not the best time of year to welcome you to Australia's top end.
Dependent on whether rains come earlier or not, there could be some sections of Kakadu closed off and whereas some tour companies do start scaling back operations ( just less visitors and Kakadu conditions ) there are a few that do wet season tours but as stated in post #1 it is more likely that most of Kakadu will be very dry and perhaps very little if any water flowing at waterfalls and doing any hikes could largely be forgotten about because of the heat, exhaustion and rapid dehydration that can occur - whatever you do in the top end, get yourself some electrolyte tablets for adding to your drinking water as water alone does not replace the minerals you sweat out and their loss can make you feel a bit off very quickly.
It is a longish drive into Kakadu and out again on top of what you can get to so also make sure you get on a tour that has airconditioning, I having seen some of the larger 4WD vehicles with forward facing seats and aircon, people probably staying at air conditioned accommodation too as against the roughing it in smaller Toyota troop carrier type 4WDs with side facing benches, no aircon and camping in swags and tents - comfort does cost but in late November, I would pay for it.
You may also want to consider having a look at Litchfield NP as an alternative to Kakadu.
For your flights, I reckon there is a far better option than what you are considering:
. Fly Darwin to Alice Springs or Uluru direct if that is what you want to see.
. Then from Uluru fly to Brisbane.
If your quickie to Cairns is just to see the GBR, a lot of the reef in the northern parts has suffered from Coral Bleaching and you can find some locations as good if not better down towards the southern end, there being Heron Island you can stay overnight at and that is accessed from Gladstone just an hours flight north of Brisbane or for a similar length flight to Bundaberg you can do a day trip out to Lady Musgrave Island from either Bundaberg or Town of 1770 ( so named because that is where Captain Cook first landed in Queensland in 1770 ).
Alternately and for a not insignificant additional expense, you could fly to Hervey Bay and and do a trip to Lady Elliot Island, they having a combination package available for a couple of days there as well as a couple on Fraser Island.
It can be considered expensive but with what you would save on airfares flying Darwin to Cairns, Cairns to Alice Springs and then to wherever, perhaps you could accommodate it in your budget.
The bonuses you will have being:
. You get to the centre before it really gets red hot.
. Better weather and reef conditions
. With a bit of luck, there may still even be the odd stragglers of Whales heading back south for the summer.
( I have seen a mother whale with calf in the southern GBR area as late as the first week of December ).
And yes, on the legs where there are cheaper seats, cheaper seats always get booked rather quick ( just our human TA nature ), so once you have settled on a plan, get your flights booked ASAP if you want to save a bit.
As for flexibility, that can be OK but for the time of the year you are considering, you will not want to be hanging around too long in the top end or the centre.
Also make sure you have some lightweight loose fitting long sleeved/legged cottony type garments and a broad brim hat ( maybe bought in Darwin to avoid travel crushing ) to protect you from the sun, plenty of sun cream and insect repellant ( also available in Darwin ), Bushmans a good brand for the latter and to save yourself from not liking the attempt to acquire a taste of flies, get yourself a fly mesh to hang off your broad brim hat and you will soon enough acquire the skill of eating a sanga inside the mesh.