Hay River

Not with a trailer, but Hay River Tk is a piece of cake.
You are driving with the dunes, rather than travelling east west in the region, when you do have to cross many dunes.

One person in our group had a Tvan behind a Troopie when we did it in 2005. He had no problems but they had 4" of rain about 4 weeks before we did it so the sand was firm.
Theres a good video of someone's adventures towing on the Hay River track from 4 years back:

I will be doing the Hay River Track in 2 weeks. Three DMax's did it towing trailers, if you google "Hay river track DMAX" you should find the article on the outbacktravelaustralia.com.au website.

A friend towing a camper trailer was with us on our Hay River journey. The sand was extremely soft (this was in 2010) and it did it quite well. We went from north to south as the dunes had a slightly lower gradient that way. Saw the wildflowers better that way too. Great trip

I took a TVan across, but I did not "drag" the trailer. (sorry, but it is an expression that may lead to assumptions)
As others have said, it was relatively easy, but towards the southers parts where you cross the dunes we dropped our tire pressures considerable which allowed us to "glide" the trailer across ;-)
Seriously, the hardes paret of the Hay is the bit of the Simpson you do to get to/from the Hay.
Cheers