Rambling tirade on furry creatures (8)

I believe the answer is:

rodentia

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'rambling tirade on furry creatures' is the definition.
I can't tell whether this defines the answer.

'rambling tirade on' is the wordplay.
'rambling' indicates anagramming the letters.
'tirade'+'on'='tiradeon'
'tiradeon' anagrammed gives 'RODENTIA'.

Can you help me to learn more?

(Other definitions for rodentia that I've seen before include "animals with strong teeth" , "natural order" , "Order including rats, mice, etc" .)

I've seen this clue in The Independent.

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