How Ted, a toddler, faked being in a deep sleep (4,2,3,5)

I believe the answer is:

dead to the world

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'in a deep sleep' is the definition.
I know nothing about this answer so I can't tell whether this works.

'how ted a toddler faked' is the wordplay.
'faked' indicates an anagram (I've seen 'faking' mean this).
'how'+'ted'+'a'+'toddler'='howtedatoddler'
'howtedatoddler' is an anagram of 'DEAD TO THE WORLD'.

'being' is the link.

Can you help me to learn more?

(Other definitions for dead to the world that I've seen before include "Fast asleep" , "Sound asleep; unconscious" , "Sleeping" .)

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

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