Carol backs exemplary solo lifestyle? (9)

I believe the answer is:

singledom

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

'solo lifestyle?' is the definition.
I can't judge whether this definition defines the answer.

'carol backs exemplary' is the wordplay.
'carol' becomes 'sing' (I've seen this in another clue).
'backs' says the letters should be written backwards.
'exemplary' becomes 'model' (model can mean exemplary or ideal).
'model' written backwards gives 'ledom'.
'sing'+'ledom'='SINGLEDOM'

Can you help me to learn more?

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

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