Hi Clara, and welcome to Australia, well a virtual part of it anyway!
First you'll need to see a General Practitioner, which everyone here refers to as a GP. This is as simple as a Google search 'GP near me'. The costs are as @Zoffiel says above. If Sweden has a reciprocal health care agreement with Australia, add 'bulk bill' to that search and you will see a doctor for free.
Your GP will refer you to an oncologist. This is a formal process where you are given a letter to take to the oncologist. If you like the oncologist and are happy to work with him/her, you can ask your GP for an indefinite referral so you don't have to keep getting a referral every few months.
I am about to start Letrozole on Friday. I was still menstruating when I was diagnosed so my oncologist has told me that I will have a blood test every three months to see what my FSH & LSH levels are. If they're trying to start my periods again I'll have a Zoladex injection every month. Given your age I'd say you will definitely have blood tests but I couldn't say the frequency.
Seeing a private oncologist will definitely cost you money. Again, with the reciprocal agreement, you may be eligible to see an oncologist in the public system. However it removes choice and there may be waiting times.
Good luck with the move. I hope it all goes smoothly, and that life in Australia will be good! Let us know how you get on. Kate xox
