Beth I would not try it in a small car but that's me. I went on a day/evening tour from Mildura 'cos it gives you access to the whole shebang - no access to the dunes - you can only look from a locked gate.
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Esmeralda
It aint over until the fat lady sings, and I dont feel like singing just yet!
A 4X4 is not "required" to visit Mungo National Park. However, the roads are unsealed, red dirt/clay roads. They are kept fairly well graded and the local landowners use them regularly. A 2WD would have no problems in the winter months - as long as there has been NO rain. It does not take very much rain to make the roads slippery and mostly impassable, even in a 4X4.
I have been there a few times ... coz I LUV it!
I have always had a 4X4 with campertrailer. The last time I visited, there was unseasonal rain after we got in to the campground. ALL the roads within the park were impassable. The top inch or so of dirt/clay became slippery mud and we were confined to the campground and walked. It took three days for the place to dry out sufficiently for the tourist bus in there to be able to get sufficient traction to get out.
If you take it sensibly and quietly up from Mildura with a 2WD it would be OK ... but take extra tucker and water in case it rains while ya in there.
I've done a fair bit of dirt/mud driving, although not always by choice. Yes Gerty, clearance is usually the tricky bit with a 2WD.
We got caught at Jondaryan with unseasonal rain, and that's blacksoil country. Sticks like the proverbial once it's rained on. Lots of vehicles, not only 2WDs, had to be pulled out by the tractor. Including moi and sis & bil.
I'll add it to my list and take all that into account.