For furnished rentals, although it's not kept updated quite as often as realestate.com.au, I find the keyword search feature on www.domain.com.au is very useful. You can put in "furnished" as a key word and take it from there.
It does occasionally trip itself up by including anything with "Unfurnished" in there (d'oh) but there are a few listed that are furnished: http://www.domain.com.au/Search/rent...ords=furnished
Although most on there are longer term rentals, it is worth contacting a few real estate agents and asking if they have anything for a couple of months. Donna, who posts on here as Jarnasa, also handles short term furnished rentals and has a few properties that are more central. You may need to rent short-term away from your eventual choice of suburb, and use the time to secure a longer term unfurnished rental for when your furniture arrives. If you haven't already looked there, there is a section on here that has ads for various furnished rentals: http://www.pomsinadelaide.com/forum/...d-rentals.html and I also know of someone that has furnished short term apartments around Frewville and Glenunga which are on the eastern side http://www.accommodationadelaide.com.au/