To answer the question in the simplest way, the cockatoo has a backbone.
However, there is more to it than that, especially given that there are two invertebrate chordate groups - Urochordata (tunicates) and Cephalachordata (lancelets) - whose backbone is not in the form of actual vertebrae.
As Chordates (or members of the phylum Chordata), cockatoos share the following characteristics:
dorsal nerve cord which is a bundle of nerve fibres which runs down the back. It connects the brain with the lateral muscles and other organs.
notochord which is a cartilaginous rod running underneath, and supporting, the nerve cord - in the case of the cockatoo, a spine.
post-anal tail - an extension of the body past the anal opening. (This feature is not always present in some adult Chordates such as frogs and humans, but it is present in the cockatoo.)
Pharyngeal pouches - Chordates, at some stage of their life, have pharyngeal grooves and pouches that develop into other essential parts of their anatomy.
Dogs are in the Chordata phylum, therefore Pit Bulls are in the Chordata phylum.
Birds belong to the phylum Chordata, specifically the subphylum Vertebrata. This means that birds are vertebrate animals with a backbone.
Chordata phylum
Phylum Chordata.
The phylum of a stingray is Chordata.
The phylum of a dove is Chordata.
chordata/chordates
Cows belong to the phylum Chordata.
The eagle belongs to the phylum Chordata.
A llama belongs to the phylum Chordata.
Apes belong to the phylum Chordata.
Vultures are found in the "Chordata" Phylum.