Over-protect and move a tip-top animal (5-4)

I believe the answer is:

nanny-goat

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'animal' is the definition.
(I have seen 'Female animal' mean 'nanny goat' so perhaps 'animal' could also mean 'nanny goat')

'over-protect and move a tip-top' is the wordplay.
'over-protect' becomes 'nanny' (I can't explain this - if you can you should give a lot more credence to this answer).
'and' says to put letters next to each other.
'move' becomes 'go' (to go is to move).
'tip-top' becomes 't' (top of the word 'tip-').
'nanny'+'go'+'a'+'t'='NANNY-GOAT'

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

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