At SYD there will be maxi-cabs (taxi) that can take 4 people with luggage. Or the shuttle. However Uber will cheaper.
Or
https://prioritytransfers.com.au/
The Great Ocean Road (GOR) is south west of Melbourne. Basically on the coastal route from Melbourne to Adelaide. The coastal route from Sydney to Melbourne is the Princes Highway. 99% of the time the road is inland and some distance away from the coast. Allow 2 to 3 days to drive the Princes Highway to allow some stops. Still a far better drive than the direct Hume Highway route which now is now mostly a boring dual freeway, with many large trucks.
Phillip Island is south of Melbourne. So if driving the Princes Highway route (or Gippsland highway) better to turn left to Phillip Island and stay over night. The main PI attraction is the penguins at dusk. Leave for Melbourne mid morning to avoid the morning suburban traffic.
To get from Melbourne to the Blue Mountains you need to drive Melbourne-Albury–Wagga Wagga-Young-Cowra-Bathurst-Lithgow-Kotoomba. Allow 2 days (or more) if you want to stop along the way.