Quite simply Rex is the only surviving independent airline in Australia at the moment, and it's model isn't exactly full service. Not strictly talking about RexJet or whatever its called either, I mean Rex in general. Tiger and J* are/were subsidiaries of a mother company. J* might pretend to be separate from mother but it's quite clear they operate with shared interests. Q-Link is the same boat as J* and co.
There are some distinct differences between operating a separate viable/successful airline and buying/creating subsidiaries that are tools for either blocking competition, stifling industrial unrest or such. Southwest is the example of a successful LCC, Ryanair the ULCC. J* and Tiger just prove that we need scope clauses in Australia and are not really viable in their own right, not in the long term, the revenue either has made is pitiful with hopeless ROI.