When we made a circuit in 2019 we built the timing around the seasons and it worked well, although we plan to go back to Kakadu in "the wet" in the future for a very different experience there. I think your timing is about right, at least for the way we travel.
So, the drivers, as others have noted, are to avoid summer in the north and centre (if you want to travel into the Simpson for example you won't get a permit in the summer). For Victoria you're better off in the summer so you would want to be in Melbourne in January or February.
I think that if I were doing your trip I'd start in Melbourne in February/March, spend some time in Victoria, explore the southern part of SA then work my way through NSW to Sydney and then north to Cairns to arrive around May, then west to Darwin/Kakadu, GRR in June/July, and south through the Red Centre in July/August, arriving back in Melbourne in August/September.
PS: anticlockwise is shorter.
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