I would recommend to cycle from Adelaide to Darwin, its better because of the wind which cames from the soth most of the time.
Oh yes, I can confirm this statement. We were doing up to 150 km a day coming from the south, peddalers coming from the north were doing up to 80 km, always fighting against headwind.
My experience is the wind is coming from southeast, so I also can't recommend the route from Tennant Creek to Cairns, which we wanted to do first.
I woun´t buy a bike in Australia. Take your time, search a good airline and take your own one. For example "Malaysian Airline" is good when you take you bicycle with you. Have a look at the hompages of the airlines - most of them have informations there about conditions to carry a bike.
And I also wouldn't buy a bike. They have good bikes there, sure, but in the middle of nowhere you'll be happy to know what you have and which tools and replacement parts you need.
Happy planning out!
Katrin