We will be visiting late March for around one month. Looking to start off in Perth for around 3 days, are there any must sees here? Next moving on to Melbourne, around five days and want to visit Twelve Apostles and see penguin parade at dusk. Is public transport adequate at Perth and Melbourne or do we need a car at one or both?
We are planning to drive from Brisbane to Port Douglas, allowing around ten days and would like to visit Whitsunday Islands. What is the best way to travel to the islands from the mainland, can you take a car?
Many thanks,
Rich.

You can take a 4WD only to Fraser Island (its all sand) and Magnetic Island off Townsville has sealed roads, vehicular ferry from Townsville is expensive. Cheaper to leave car on mainland; there's a bus sevice on the island. Everything else reached by boat, plane or helicopter. Shute Harbour, near Airlie Beach is mainland departure point for most Whitsunday Islands where parking is available.

From Port Douglas/Cairns, which are closer mainland points to Great Barrier Reef, it takes about an hour and a half to outer reef in a fairly fast boat.

Sorry, I might learn to edit one day, parking is at Shute Harbour of course, not the Whitsunday Islands.

In Perth, there are a number of free bus routes around the CBD so it is quite easy to get around without a car. Kings Park is a must - there is a nice restaurant for lunch or dinner, or buy snacks and sit and enjoy the view. We've always enjoyed the boat trip from Perth along the Swan River to Fremantle.
Out of Perth, you could take a day trip to New Norcia, about 100 km north of Perth - it's an old Benedictine settlement with churches etc and very interesting.
In Melbourne, there is a free tram service around the CBD. If you are going to see the penguins at Philip Island, I'd suggest taking a tour as the penguins don't come into until dark so you will be facing a long trip back to the city late at night. You can see penguins in Port Philip Bay - the boat goes from Southbank and I think includes a BBQ.
The best way to see the Great Ocean Road is to hire a car, simply because you can stop and look whenever you feel like it. If you can, take two days and stay overnight at Port Fairy. Apart from the Twelve Apostles (not really twelve!), go to Loch Ard, and visit Mariners Lookout at Apollo Bay for great views.
If you go for the two day option, you could return to the city via Ballarat, or better still, make it three days and have a look at the Grampians National Park on the way.
Hope you enjoy your holiday.

Surich, here is a great website for information on Perth and WA. http://www.westernaustralia.com/en/
After seeing this website you might consider spending more time in WA 8-)

There is a ferry service to some of the Whitsunday islands - I can't remember the details - try google.

But the best way to see the islands is to take a boat trip (I won't call it a cruise). There are day trips and there are overnight trips - all sorts of overnight trips 2 days 2 nights; 3 days 2 nights, etc. etc. There are maxi yachts, and sloops. There are tall ships and modern catamarans.

Some years ago I took a 3 day 2 night trip on a monohull that carried only 12 pax with 2 crew. Wonderful. You get to snorkel from the boat, and sail between the islands, and stop at Whitsunday Beach, and a morning on another island for a bit of a bush walk.

Google again - try Prosail, or Tallarook, or just a generic search for "Whitsunday sailing". It will give you some idea of what is available.

As others have said - you do not need a car in Perth or MLB. A must see for me in the Perth area in the time you have available would be Rottnest Island.

Happy travels.