Would I be allowed to take my sulphur crested cockatoo with me?
This is from their website. "No pets (except service animals) allowed and visitors may not leave pets in their cars."
Very much doubt it.
If you have any questions you can always contact them at their web site. But I believe there is a no pet policy, that is for their protection and the animals protection.
I don't believe you can take any pets into the Gardens.
The answer earlier applies. If you're serious, call the garden.
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