Australian consumer rights exist independently of the warranty offered by the producer. My guess is that it's perfectly legal not to offer an explicit warranty

Australian consumer rights exist independently of the warranty offered by the producer. My guess is that it's perfectly legal not to offer an explicit warranty (or one with very short duration), however, it is illegal to refuse refund/repair when reasonably requested. Crucially, the lack or expiry of an explicit warranty is not a valid defence -- it's about the product meeting quality expectations given its cost.