You are lucky. And let me stress this. Lucky. Because this is research you do before you move continents.
As you are Australian, you are exempt from the normal rules that apply. You do not have to go back to your home country and apply from there.
- You need to go to your landlord (Vermieter) and register with them.
- With the paper you got from your landlord, you go to the civil administrations office (Bürgerbüro) of your city and register there.
- With that paper you go to the foreigners office of your city (Ausländerbehörde) get into a long line with all the others and when you get an appointment, you show your marriage certificate and passport. You will also need to prove a sufficient grasp of the German language (commonly called "Level A1"), either through a certificate and a quick oral test there (basically just the clerk asking you simple questions like your name and birth date in German and expecting you to answer in German to make sure your certificate isn't a total self-printed fraught) or if you actually do speak good German, you can demonstrate it there without the need for a certificate (for example by just going through all of this in German yourself).
You need to be at all those steps in person. I'm not sure if your husband is required, but it will help a lot to have somebody who knows his or her way around the German bureaucracy.
If you don't know German yet, the biggest problem might be A1. Try to find a course, work on it and try to do all that stuff above immediately. German Amts are ok, as long as you are prepared, do everything they say to the letter and stay in touch and work something out with them. If you come on the last day and something is missing, that's not going to end well.