Boy having party with little Charlie (7)
I believe the answer is:
'boy' is the definition.
'party with little charlie' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'with' is a charade indicator (letters next to each other).
'little' becomes 'mini' ().
'charlie' becomes 'C' (phonetic alphabet).
'having' acts as a link.
(Other definitions for dominic that I've seen before include "Priest" , "Man's name" , "Man" .)