Who controls the federal elections, is there an organisation?
The Australian Electoral Commission (AEC) is responsible for conducting and controlling federal elections and referendums, and maintaining the list of all people entitled to vote (the electoral roll). The AEC is an independent government agency.
People voting

Australian Electoral Commission
Description
Three people are in a polling place completing their ballot papers in cardboard voting booths. Each voter is separated in their own booth to ensure their vote is secret.
Permission should be sought from the Australian Electoral Commission (AEC) for third-party or commercial uses of this image. To contact the AEC email: media@aec.gov.au or phone: 13 23 26.