Hello @FraserY, welcome to Singapore!
It is almost impossible, if not extremely difficult to import your vehicle into Singapore. Unless it is a classic model, which you can then import under the Classic Registration scheme, you would almost certainly be better off selling your Ducati in Australia and buying another one in Singapore.
You can find a price list (albeit a few months old) of the official Ducati Singapore dealer here in Singapore located in the thread below:
The current Monster 950 is retailing for S$39,800. If you do swing by, mentioned SingaporeBikes.com and i'm sure the guys there will take good care of you!