Sydney is much, much faster than that (4-6 months if I remember correctly). Remember, processing times on the website are the times that it takes 80% of application to get through in that amount of time or less. However, if you do the medical just before you submit your application, you could probably land when you were planning (the COPR is valid until the medical expires, which is valid for 12 months, unless the principal applicant's passport expires sooner).
US citizens are visa-exempt, so they came with a visa-exempt passport, which is not a tourist visa. If you hold an Australian passport, then you're visa-exempt too.
