It's a long way Laura and though I haven't been in that area for a while I've done plenty of longish trips inland Queensland through NSW to Victoria and it's the boredom aspect that'll get to you a bit on a lot of those legs.
Weatherwise it is the best time of year to go and if your car is in good nick and you have auto club highest level membership to help out if you do have any major nreakdowns then no reason why it cannot be done and also a good idea to skill up on vehicle basics maintenance.
You might even want to put out some notices on various sites, needaride - travel cheaply around Australia a lot easier
for instance if you wanted to try and get company and putting details of the trip on hostel notice boards a few weeks beforehand may get you some travellers interested = at least share the fuel cost!
One way to lessen some of the Boredom but up the challenge would be to consider the Oodnandatta Track route - Oodnadatta Track @ ExplorOz
You'll miss Coober Pedy, not necessarily a huge loss and get the option to see more of the Flinders without backtracking and aside from the history of the Oodnadatta places like The Iga Warta Experience
but though you could manage it in a 2WD vehicle, you would want to have a robust 2wd and have capacity to carry sufficient fuel, an extra spare tyre plenty of water and some basic winching equipment to get yourself unstuck as insurance.
I'd reckon that three months is not a bad time frame, allow you to take your time, stop here and there and absorb the experience and the outback.
One thing that'll need to be checked is inland floodwaters situation, a lot of the Queensland flood waters finally get to Lake Eyre which may get a bit full this year and that only happens a few times each century, noy sure how far past Lake Eyre that could extend.
Could be a great year for inland wild flowers with the rain had.
Road Conditions | Benefits & Discounts | RACQ
or similar sites will allow you to check on road conditions.