Anaesthetised a cross marsupial (6)

I believe the answer is:

numbat

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'marsupial' is the definition.
(I know that numbat is a type of dasyurid)

'anaesthetised a cross' is the wordplay.
'anaesthetised' becomes 'numb' (I can't justify this - if you can you should believe this answer much more).
'cross' becomes 'T' (shape).
'numb'+'a'+'t'='NUMBAT'

Can you help me to learn more?

(Other definitions for numbat that I've seen before include "one bright-eyed and bushy-tailed?" , "Australian native" , "insectivore" , "Termite-eating marsupial" .)

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

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