you have to contact an animal transport company in your city, they will give you a quote on the cost of the flight, the hire of a crate, unless you have one yourself. There are also rules on how long the animal can travel without a break, by memory I think they have to stay in singapore overnight to eat/drink.
When you reach australia, your animal must be kept in quarantine for 30 days, and that costs you a weekly fee. First you get a importation number, then you have to prebook your spot there, so your animal arrived at the correct time. Sorry, but it is not as easy as you seem to think. Because Australia has so few animal diseases, we are very fussy about allowing animals into the country.
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