A thousand and one doctors for a NSW town (5)

I believe the answer is:

kiama

I'm a little stuck... Click here to teach me more about this clue!

'nsw town' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'a thousand and one doctors for a' is the wordplay.
'a thousand' becomes 'K' (synonyms).
'and' is a charade indicator (letters next to each other).
'one doctors for' becomes 'iam' (I am not sure about this - if you are sure you should believe this answer much more).
'k'+'iam'+'a'='KIAMA'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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