Mandy... what I can give you is some generalised information. I am a family lawyer working in Victoria, and I think you're in QLD.

Please obtain professional legal advice for your own circumstances. The following is NOT a substitute for independent legal advice nor is it guaranteed to be absolutely accurate as I have been on maternity leave for nearly a year now.

In Victoria, the general process is as follows:

1. Ensure that the relinquishing parent will consent to the adoption.
2. Contact DHS (Department of Human Services) and talk to them about how to go about the adoption. They will prepare a report and organise the counselling for the adoptive parents, child (if applicable) and relinquishing parent. One requirement of the adoptive process in Victoria is that the step-parent and the parent must have been in a relationship for more than 2 years (they don't HAVE to be married, but it certainly helps).
3. Note that DHS generally do NOT approve step-parent adoption. It is only in exceptional cases (ie imminent death of one parent) that adoption is approved. I think there are about 3 step-parent adoptions in Victoria each year.
4. If adoption is approved, an application must be made to the Family Court of Australia to allow the step-parent to adopt the child. If this is not done, the relinquishing parent can still bring applications for contact and residence in relation to the child, as the relinquishing parent will still be considered, under the Family Law Act, a parent of the child. Essentially the child will have three legal parents.
5. If the Family Court application is successful, then an application must then be made to the County Court (District Court in QLD). A number of forms must be filled out including affidavits of the whole story etc etc. A judge will then decide whether or not the adoption will be allowed to proceed.

As I said, it's a complicated process, and you need to obtain advice from a independent lawyer who is familiar with adoptive processes in your state.

Best wishes. Email me if you have any other questions.