Bomb dog cross with insect (9)

I believe the answer is:

doodlebug

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'bomb' is the definition.
(I know that doodlebug is a type of cruise missile)

'dog cross with insect' is the wordplay.
'dog cross with' becomes 'doodle' (I can't justify this - if you can you should give a lot more credence to this answer).
'insect' becomes 'bug' (bug is a kind of insect).
'doodle'+'bug'='DOODLEBUG'

Can you help me to learn more?

(Other definitions for doodlebug that I've seen before include "may be cruise missile" , "German bomb otherwise known as a V-1" , "WWII flying bomb - mineral detector" , "World War II flying bomb (V-1)" , "WW2 rocket" .)

I've seen this clue in The Independent.

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