I actually rent my property out using Airbnb. I don't live in Melbourne and have a cleaner who re-stocks and cleans ( $85 per clean). Can you fly back and forth to Melbourne for that price?
I have a keyless entry system so I don't incur an extra charge for face to face check ins. That way guests can self check in which makes it simpler.
I have a number of tradies that I use if anything goes wrong. I think that you might be a bit too optimistic in your pricing. There is a lot of competition in Melbourne. My own pricing is $119 per night for a one bed in Toorak and I have difficulty filling my calendar.
There are a lot of companies which you can use to manage your apartment in Melbourne. They charge a managment fee of 12% which does not include cleaning, linen, supplies. I used one of them but was very unhappy with their cleaning services ( as were my guests ) as well as their ability to meet and greet the guests in a timely manner. It was a waste of my money , from my own very limited anecdotal experience.
In the end , you might be better off sticking with a property manager for a long term rental if pricing is an issue.