All of the information would be contained in this Boeing Technical documentation:
http://www.boeing.com/assocproducts/aircompat/acaps/737sec3.pdf
Ozjet run 737-200 Advanced planes (737-229 JT8D-15). The are covered on page 87 of the manual.
SYD-PER is 2038 miles.
MEL-PER is 1679 miles.
If I am reading the tables correctly, a normal loaded O7 plane would not be able to do much more than about 2200 miles without refuelling. More likely the total would be not much more than 2000 miles depending on load.
That would not allow much leeway when flying to a town such as Perth. Add in issues like storms, ATC getting the plane to circle etc and requirements for how much fuel must be spare onboard, and I don't think it is viable. I'm sure OzJet are crunching the numbers right now working out if it is possible or not.
Of course I can be totally wrong, and am open to comments. However, there are also other logistical issues with Perth. For example the turn around time (they would need more planes to handle the flying time) and whether there is enough Perth demand for the service. Note that BNE is the third biggest airport in Australia after SYD and MEL, and that the three biggest airport pairs are MEL-SYD, BNE-SYD and BNE-MEL.
This leads me to think that a MEL-BNE or SYD-BNE flight is next on the agenda. More likely than not, they will start to operate the BNE-SYD-MEL triangle depending on their planes.