Creature that's said to be part dog, part duck (9)

'creature' is the definition.
(cockateel is a kind of creature)

'said to be part dog part duck' is the wordplay.
I cannot really see how this works, but
'said' could be 't' (I've seen this in other clues) and 't' is present in the answer.
'part' could be 'cock' (cock is a kind of part) and 'cock' is present in the answer.
This may be the basis of clue (or it may be nonsense).

'that's' is the link.

Can you help me to learn more?