We travel with our scripts and most of any meds we have are in blister packs with the branding on it. The ones that don't we take the brand and directions off the box in the small sandwich bag with the pills.
Once we asked the chemist for a smaller plastic container with the brand, directions on it., we haven't bothered since as we have never had an issue.
We haven't used a transfer service in Sydney as we use uber or the trains, however we have used various transfer services elsewhere. Joyride comes to mind but you could also google transfer services for Sydney and just compare pricing and services, I.e shuttles or cars, etc.
Perhaps it would be best to have a second stop closer to Phillip Island. That way you could have a visit at Eden, stop at Mallacoota or Orbost for the night, then travel through to Port Albert or Port Welshpool for the night. You will then be at Phillip Island by lunch.
Just research each port individually at a time, work out what you want to do and then proceed to book it and move onto the next port. I love the research and planning.