hi, Ive just spent some time researching the answer to that same question.
Apparently no cases of lyme in Australia have been proven.
From the Department of Medical Entomology" site who has spent some time trying to find lyme in Australia. They have spent some time and many studies, looking to prove lyme exists here but so far havent found the proof.
"Lyme disease (LD) is a tick-borne zoonosis caused by the spirochaete bacterium, Borrelia burgdorferi. Since the disease was first recognised in 1975 it has become the most frequently reported human tick-borne infection worldwide. It has been reported from every continent (except Antarctica) although doubt remains as to whether it occurs in the southern hemisphere in general, and in Australia in particular.
LD is transmitted to humans by ticks. Larval and nymphal stages feed on infected reservoir hosts, acquire the organism and then, after moulting to the next life stage (nymphs and adults respectively), pass on the infection to humans and other animals. In the northern hemisphere, small placental mammals are reservoir hosts. The only species of ticks shown to be competent vectors of B.burgdorferi to humans belong to the Ixodes persulcatus complex, including I. scapularis and I. pacificus in the United States, I. ricinus in western Europe, and I. persulcatus in eastern Europe and Asia. No species of this complex exist in Australia.
"From 1988 to 1994 at Westmead Hospital, 78 (1.8%) of 4,372 from local patients with suspected Lyme Disease were positive for IgG by ELISA and IFAT. All 78 were tested by WB, using North American and European strains of Borrelia; 46 sera showed one or more bands. NONE, including those with putative late stage disease, showed more than 4 specific bands and thus were ALL NEGATIVE by international criteria"
It goes on to explain that that is the amount of positive IgG tests of this type that is expected to turn up if there is no lymes. Apparently those tests always get a low percent of false positive ones, due to cross contamination of other bacterias which end up showing up as a positive IgG result hence it needs to be followed up with the Western immunoblot (WB).
But by that.. obviously they've really tried to find a true positive lyme case in those who could have lyme via the symtoms (4372 people..so no small study!).. but no positive lyme case has ever been found.
Maybe you have something like CFS.. have you been tested for other tick carried things.. eg the rickettsia species. I have Chronic-Fatigue-Syndrome with lot of neuro symptoms so my specialist had me tested for rickettsia species.
"Rickettsia species are carried as parasites by many ticks, fleas, and lice, and cause diseases such as typhus, rickettsialpox, Boutonneuse fever, African Tick Bite Fever, Rocky Mountain spotted fever, Australian Tick Typhus, Flinders Island Spotted Fever and Queensland Tick Typhus  in human beings. "