Yes, there are special statuses for spouses and children (dependents) of E-3 visa holders which allows them to travel with you on an E-3 (whether they are Australian citizens or not).
For spouses (must be married – de facto doesn't count in the US), you automatically receive working rights on the E-3S status. For children (under 18) there is a special E-3Y status which allows them to study, attend school, but not work. More information about these visas can be found here.