Hi Michael,
I took my offroad camper to Mitchell Falls campground last year, if the trailer is strong and you are willing to go slow and lookout for larger holes it is ok but it would be a more comfortable drive without a trailer.
I did have a problem with the brakes on the trailer, the pads had worn at the mounting points and started jaming on and had to disable them until I got to Broome and fixed them.
We did come across a family in a Prado along the way that had left thier trailer at Drysdale and had a few issues like a broken battery mount and bashplate and they had left thier tools and spares in the trailer, fortunately we had what they needed. If you do leave the trailer make sure you grab everything you need.
If I was doing it again I would leave my trailer at Drysdale and tent it.
Cheers,
Tony