1a. Next step is to immediately get yourself an ID card from Skatteverket.
1b. Then get yourself a Swedish bank account, if you don't already have one.
1c. Australia has a reciprocity agreement with Sweden, if I understand it correctly, so it might be worth your while to fill out: https://www.google.se/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjnm5iShd7VAhUqIpoKHXvmATsQFghPMAQ&url=https%3A%2F%2Fwww.forsakringskassan.se%2Fwps%2Fwcm%2Fconnect%2Fd977fbe5-b805-4771-97a2-073d9d17fc8d%2FFK5456en_014_F_002.pdf%3FMOD%3DAJPERES&usg=AFQjCNG7heZpVTM2piyi6iNI6THe3LXuFA and apply for a European Health Insurance Card. It's really useful if you need health care in another EU country, and it also establishes contact between the Försäkringskassan and yourself.