Is it a fibre to the home connection, or is it using the existing copper telephone cable (“fibre to the node”)?
If it’s fibre, then my understanding is that it can only be moved by NBN Co. You log a request through your service provider. I have heard that under some circumstances, NBN Co will do one relocation at no charge, but take this with a grain of salt.
There’s a brief mention on page 11 of this document:
https://www.nbnco.com.au/content/dam/nbnco/documents/nbn-fibre-user-guide.pdf
If it’s copper, then any registered cabler can do the move and it shouldn’t cost much.