Australia operates under a ‘first to use’ (rather than a ‘first to file’) wherein the first to use a trademark in Australia obtains rights under the common law. The first to use a trade mark as a "badge of origin", that is, to identify as the supplier of the goods and services in the course of trade, owns the trade mark. Not the first to register it.
Therefore, if another person has used the trademark before you as a trade mark in the course of trade, they have an earlier and better right to the trade mark than you under the common law. In sum, the first person to use the trade mark in the course of trade or, if there is no use, to apply for registration, is the owner in Australia and is entitled to seek registration.