Dorothy Dunnett 
Operation Nassau [PDF ebook] 
Dolly and the Doctor Bird ; Match For A Murderer

Dr. B. Mc Rannoch is in the Bahamas with her father who has moved there from Scotland because of asthma. She is a savvy and tough young lady who shows much independence of mind and spirit. However, when Sir Bart Edgecombe, a British agent who has been poisoned with arsenic falls ill on his way back from New York, she becomes involved in a series of events beyond her wildest imagination. Drawn into an espionage plot where there are multiple suspects and characters, it is only the inevitable presence of Johnson Johnson that saves the day. As with all of the Johnson series, nothing is quite as straightforward as it at first seems, and there are many complicating factors to grip the reader as well as the added bonus of another exotic location.