It is certainly possible, and in a month you could certainly cover some nice coastline.
From Sydney south is quite nice, down past Bateman's Bay, Merimbula, Eden, into Victoria, Wilson's Promontory, Port Philip Bay (Melbourne area), Great Ocean road, 12 Apostles etc.
There is some airspace to consider, particularly around Sydney itself, Nowra (Naval Air Station), East Sale (RAAF) & Melbourne, so get the charts (have a look at airservices.gov.au, you'd want WACs, ERCs, VTCs; the place you're hiring from should be able to help out, also an ERSA (Enroute Supplement Australia) with airfield details (particularly fuel availability).
I'd suggest the weather's probably going to be OK that time of year.
However, the water's fairly cold down south and significant stretches along the coast don't have much in the way of forced landing options.
Also, get in early for sorting out your licence validation with CASA, particularly as there's a big security hoo-ha going on at the moment about having a special police-checked card to get into any security-controlled areas of aerodromes.
Have fun.
