Love, child, is her undoing (7)
I believe the answer is:
cherish
'love' is the definition.
(cherish can mean to love or treasure)
'child is her undoing' is the wordplay.
'child' becomes 'ch' (abbreviation for child).
'undoing' is an anagram indicator.
'is'+'her'='isher'
'isher' with letters rearranged gives 'erish'.
'ch'+'erish'='CHERISH'
(Other definitions for cherish that I've seen before include "Hold dear, be fond of" , "Hold dear -- he's rich (anag)" , "Protect and care for lovingly" , "Nurture (a hope)" , "Hold dear, treasure" .)