Do I have to question European Union about Caribbean holiday destination? (8)

'union about caribbean holiday destination?' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'do i have to question european' is the wordplay.
'do' becomes 'must' (I can't justify this - if you can you should give a lot more credence to this answer).
'have' is a charade indicator (letters next to each other).
'to question' becomes 'qu' (abbreviation).
'european' becomes 'E' (abbreviation e.g. EU).
'must'+'i'+'qu'+'e'='MUSTIQUE'

Can you help me to learn more?