Hi Saba and welcome to TT,
On the left of the screen there is the Travel Buddies Forum and you ought to cross post there.
Also, when you get to Darwin, mosey around to the various backpacker hostels (quite a few on Mitchell St., main drag) and even put a notice on notice boards as some people seeking travelling companions may.
In heading to Brisbane ( via Alice ), I expect it could be east coast you mean and seeing as you are a driver, you may want to check out doing a campervan relocation - www. imoova.com , they for faster stints but you might find doing Darwin to Alice Springs OK if you do Kakadu separately, also possibly people in hostels looking to do shared trips to there too.
https://www.facebook.com/groups/backpackerjobsaustralia/ is also somewhere that you might be able to find travelling companions.
Good luck.