Girl in US city understood to keep a domesticated animal (5,4)

I believe the answer is:

nanny goat

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'domesticated animal' is the definition.
'nanny goat' can be an answer for 'animal' (I have seen 'Female animal' mean 'nanny goat' so perhaps 'animal' could also mean 'nanny goat'). I am not sure about the 'domesticated' bit.

'girl in us city understood to keep a' is the wordplay.
'girl' becomes 'ann' (woman's name).
'in' means one lot of letters goes inside another.
'us city' becomes 'NY' (abbreviation for New York).
'understood' becomes 'got' (getting is a kind of understanding).
'to keep' indicates putting letters inside.
'ann' put into 'ny' is 'nanny'.
'got' going around 'a' is 'goat'.
'nanny'+'goat'='NANNY-GOAT'

Can you help me to learn more?

(Other definitions for nanny goat that I've seen before include "Butter" , "milk producer" , "Billy's partner?" , "Female farm animal" .)

I've seen this clue in The Times.

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