In a word - NO, not yet.
There have been a few requests for info about this recently because the State Government have decided to go ahead with the Crime and Misconduct Commission recommendations from the REGULATING OUTCALLS review which included a proposal to allow private sex workers to have a receptionist. However, the government haven't changed the law yet and there's no way of telling how it will be changed or when.
So the legal situation for private sex workers in Queensland is still that you have to work alone unless you hire a bodyguard (with a Crowd Controllers' Licence) but this bodyguard cannot place your advertisement or answer your phone or take the money or be your driver.
Whether you can pay a driver to do outcalls is still a grey area.
Some police from the Prostitution Enforcement Task Force (PETF) have said in the past that it is ok to pay a driver (just like you would a cab driver or a chauffeur) but only if the driver gets a fee to drive only and doesn't hold the money or act as a bodyguard.