Our damp tent, it's a painfully small place to live (6,9)

I believe the answer is:

studio apartment

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

'small place to live' is the definition.
I can't tell whether this definition defines the answer.

'our damp tent it's a painfully' is the wordplay.
'painfully' indicates an anagram (letters get injured).
'our'+'damp'+'tent'+'its'+'a'='ourdamptentitsa'
'ourdamptentitsa' anagrammed gives 'STUDIO APARTMENT'.

Can you help me to learn more?

(Another definition for studio apartment that I've seen is " Flat".)

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

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