It is probably derived from the Scottish dialect word...saxpence.
Zac is first recorded in Australian English in the 1890s.
Later it is used to mean "a trifling amount of money", as in the phrase...not worth a zac.
Australian's no longer use pounds, shillings, and pence since decimal currency was introduced in 1966, but we have long memories.
Despite the fact that there have not been zacs in our wallets for fifty-five years, the word zac, and the notion that it is not worth a great deal can still be found in Australian usage.
1945 Australian Week-End Book...
The only one who'd backed it had been his wife who'd had a zac each way.
2006 Age, Melbourne 29 August...
"When I started this...I divested myself of anything I owned", he said. "I'm not worth a zac"