Hi, I work as a mental health nurse in Melbourne, been here 4 years. Don't want to sound harsh but RNLD is not recognised here. You potentially can work as a mental health nurse as all nurses technically are general nurses when registered with AHPRA. However, you would probably have to do a post-graduate mental health course(diploma/BA etc) with in a certain time if you got a job. I do know of UK RNLD nurses who have really struggled to get work over here. I would consider getting your RMN before moving if possible. It might delay things but will make life much easier.
Nurse Prescribing: I would seriously check out if it's worth it given that you plan on moving. Check AHPRA for what they recognise. You could do Nurse Practitioner once over here if you stayed.
Sorry if this is negative sounding but I don't mean to be Having worked in Frankston/Melbourne for 4 years in mental health I can say that once you get your head round how it works it's worth it. More jobs, opportunities and money. Your UK experience will pay off in the long run. Once you've earned your stripes/proved yourself you can carve out a good career. Just remember to sell yourself at interview, seriously it is expected over here. Also just go with the flow as every service is different and it can seem pretty random compared to the NHS.
Good luck.