Are there adult bicycle passenger trailers for adults in Australia? I understand that there are kids bicycle trailers, but are there adult bicycle trailers? Specifically selling in Australia?
There are recumbent trikes available here in Australia which link together so that one tows the other - if the back person chooses not to pedal then it would effectively be a trailer, with the rear person just sitting like in chair.   These would be much lower and more stable than having a scaled-up kiddie trailer or wheelchair.   

For slow speeds and a smallish adult have a look at a 'bakfiets' style cargo bikes, there are Australian brands. 

A longtail cargo bike might be an option too, if the passenger is able to sit up on one. (I use one of these for larger kids)

Here are some of the specific brands and shops in Australia:
Linking recumbent trikes: 
Hase Kettweisel

Bakfiets style:
Kangaroo Bike (May or may not be that brand specifically ... I have seen this style bike ridden in Australia with a kangaroo logo on the side)

Longtail cargo bikes:
Kona Ute
Yuba Mundo
Surly Big Dummy
Xtracycle conversion kits

Recumbent shops:
Flying Furniture (Canberra dealer for recumbents and other interesting machines for cargo and multiple people)
Trisled (Manufacturer in Melbourne, might be worth asking them about something custom built...)