I'd give it to Taronga Zoo. The birds there don't really look much more special than pigeons, and are cared after in a controlled environment. Plus the story might make it interesting.
The problem (in this case) isn't the bird breeding, it's infections that it might carry. I can imagine it's possible there's a tonne of diseases it might carry that could be passed to the local native & agricultural bird populations that they have no exposure to.
Australia's relative isolation means that there's many diseases that local animal populations have no immunity to.
They could, ya know, return it. Or hold it for the guy to pick up.
Out of curiosity, are they willing to pay him for the seizure of property, or shall we make an international incident of it?
The owner of the bird is responsible for the bird. Therefore, the owner is responsible for the bird illegally entering Australia in violation of local customs laws, just as a dog owner would be responsible should their dog bite somebody.
I'm all for returning the bird to the owner but from Australia's perspective, the owner committed a crime. It's ridiculous to suggest that the owner should be compensated for the consequences.
The bird should be returned upon payment of a fine and reimbursement for the costs of finding, capturing and transporting the bird back to the US.
Causing an international incident would be considered a bonus for the publicity it would create.
(not condoning this, just making the observation)