There are various types of visas available for visiting Australia and most of the Visitor Visas can be lodged online but applicant must be outside of Australia at the time of lodgment.
The type of visa that you may be able to get depends on a number of factors such as, the length of your intended stay, your passport, your current location and the purpose of your visit:
Visitor visa (Subclass 600)
Electronic Travel Authority visa (Subclass 601)
eVisitor (Subclass 651)