No
I went through the koala section of the zoo yesterday and didn't see anything about being able to hold them. However, you can pay to ride on a camel and they do pony rides. In the aquarium part they do allow you to pet certain animals and reptiles.
I think this is a question you should ask of the zoo. The general admission doesn't allow for that. Perhaps if you bought a behind the scenes zoo experience or something like that you might be allowed to.
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