Seems all covered from the earlier posts, but just a couple of bits of clarification.
Medicare cards do NOT link medical information between practices. Carry a letter from your GP and if there are any significant changes (e.g. if you need to change drops) get the doctor you see to make a note on the letter or give you another note to carry. I wouldn't try to carry ALL your medical records - just a letter. You will need a covering letter to bring the eyedrops through customs anyway.
Your UK GP will not be able to write a prescription which is valid in Australia unless your UK doctor is also registered in Australia.
The cost of a standard consultation at most suburban GP practices is around $60 - about 25 pound. I'd try to check the Medicare site re cards for tourists but if the cost of shipping a 110 to Oz doesn't daunt you, you might just want to pay the money and not have to wait in a queue for a Medicare card.

