Hi Tilda,
I'm a speech pathologist
I trained 15 years ago, before the Masters programs were established, but I can imagine they do pack a fair bit into 2 years. It would help if your previous studies were in (biological) science and/or (behavioural) psychology.
Speech pathology is a great career in applied science. I love being a clinician and meeting different people with their families in the context of communication and/or swallowing difficulties. It has its drawbacks - not least is the fact it is so heavily female-dominated - and any job can have its 'rut'. Paediatric services and community based work is probably most 'family-friendly' so that limits some options if you particularly like medical aspects of speech pathology.
As for private practice, certainly you can go that way whenever it seems right to you. I would suggest contacting Speech Pathology Australia for some guidance there and definitely have some conversations with private speech paths. I don't have any experience with private practice, but it's something I think about from time to time.
Feel free to continue the conversation here or PM me.