My ob/gyn did mine too. She has done tonnes and tonnes of them and I would want someone who knows what they are doing inserting it. I think it takes some experience to get the strings right etc.

The Mirena itself is PBS, so the same cost as a script, eg the same as 3 months worth of BCP. Then you also pay the out of pocket expense for your ob/gyn, but you can probably get it done through family planning for medicare only (not sure).