I would like to book a queen room at your hotel. However, do you have drop off service to the airport at 4 am morning?
No, they haven't. But there is a tram service near the hotel that can easily connect you from and to the airport, and to other parts of the city as well,so it will be useful during your stay in Sydney. You must buy the Opal card at the airport (which is like the milky in Melbs), and charge it, then ask to the employee where you have to take the tram for the city. You'll arrive at central station and then you'll take another tram to reach the tram stop near the hotel. I don't remember the name exactly but is next to a huge car parking. Enter in it, go up to the 4th floor, then exit, cross the street and turn right, then take the first on the left and you'll finally reach the hotel :)
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