Done Katherine to the East Coast on many occasions. As long as you stay off the road between dusk and dawn, travel in the dry season and avoid a place called the "Star Inn Accommodation for Single Men" in the Isa, really shouldn't have any problems! Carry plenty of water - you can never have too much, approach emus with caution and fill up any jerry cans before leaving QLD (fuel prices jump dramatically when the roadhouse generates their own power onsite). Unless you really wanna go exploring, the most direct ways follow busy Interstate truck routes so you'll not exactly be alone out there. They have done a lot of upgrades in recent years so the roads are generally an easy drive.
Be sure to plan a stop in Elliott for a truly "unique" experience. And visit the Hoochery once you get to Kunnas!