A bad fall with Florida fodder (7)

I believe the answer is:

alfalfa

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'fodder' is the definition.
(alfalfa is a kind of fodder)

'a bad fall with florida' is the wordplay.
'bad' indicates anagramming the letters.
'with' means one lot of letters goes inside another.
'florida' becomes 'fa' (I am not sure about this - if you are sure you should believe this answer much more).
'fall' with letters rearranged gives 'llfa'.
'llfa' placed around 'fa' is 'lfalfa'.
'a'+'lfalfa'='ALFALFA'

Can you help me to learn more?

(Other definitions for alfalfa that I've seen before include "A forage plant" , "cattle feed" , "food plant" , "Lucerne, a fodder plant" , "Plant used as fodder" .)

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

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