I think you'd be OK on the Thursday night unless you have a big set-up.
There are probably three overflow campsites if you head north towards Roses Gap. Just look for the tracks heading off the road on your right (east). The first is Dead Bullock Creek (3.3km), the second is smaller (4.2km). The third one is past Roses Gap; go all the way to the Mt Zero Rd (7.7km), turn left (North) and there is a big camping area on the left a few hundred meters up the road. None of these have toilets so make sure you have the right resources to set up something adequate. None of them have water either.