I've done that run at least three times each way on the bike, I showed my usual fuel stops on the map, but I still took at least an extra 10 litres (usually 20) because of towing the trailer.
I did manage one run from Newman to Port Hedland before I had the fuel light as it's mainly downhill but I did have spare fuel just in case.
You should be able to run from Meekatharra to Newman on one tank, mine used to but I showed Kumarina as most bikes need to stop there or they won't make it.