I know the gist of his career, i.e. he founded and headed the Free Officers movement, established a network, gained sympathisers and then took advantage of King Idris' trip abroad to launch a coup and gain power.

This makes me ask a few questions. He was 27 at the time of the coup, only a captain. Why did the rest of the armed forces who weren't involved with the Free Officers' movement just let him basically become the head of state and commander-in-chief of the armed forces? Surely there must have been a fair amount of senior officers much higher in rank and not involved with the movement who would have been irked at this upstart becoming practically a general in one day.

Were there no monarchy loyalists in the Libyan army who would have opposed the coup?

And the senior military officers who approved of monarchy being overthrown, but were now being left in the shade by Gaddafi and his crew, what were they doing? If I'm a power-hungry, opportunistic general in the Libyan Army in 1969 what's stopping me from raising a brigade, removing Gaddafi and installing myself as dictator?