Big bird steps, say, into town (3,6)

I believe the answer is:

emu plains

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'into town' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'big bird steps' is the wordplay.
'big bird' becomes 'emu' (type of large bird).
'steps' becomes 'plains' (I can't explain this - if you can you should give a lot more credence to this answer).
'emu'+'plains'='EMU PLAINS'

'say' acts as a link.

Can you help me to learn more?

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

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