Dr. Hugh Westlake and his daughter, Dawn, help a diva in danger, by the Edgar Award-winning author who wrote the Peter Duluth Mysteries as Patrick Quentin.   Patrick Quentin, best known for the Peter Duluth puzzle mysteries, also penned outstanding detective novels from the 1930s through the 1960s under other pseudonyms, including Q. Patrick and Jonathan Stagge. Anthony Boucher wrote: "Quentin is particularly noted for the enviable polish and grace which make him one of the leading American fabricants of the murderous comedy of manners; but this surface smoothness conceals intricate and meticulous plot construction as faultless as that of Agatha Christie."   At the behest of a friend, country doctor Hugh Westlake retires to Bittern's Bay--a ritzy New England resort--for a holiday with his daughter, Dawn. The place is abuzz with the presence of legendary actress Daphne Winters, who has with her a coterie of young actresses she hopes to mentor. The divine Daphne soon finds her star dimmed with the arrival of Lucy Milliken, who was once her understudy and has since usurped Daphne's role as America's sweetheart. Almost immediately, Westlake can see both cats sharpening their claws.   Then, one of Daphne's wards is struck down by poison--one of the actress's greatest fears. And when recurring incidents play upon her other fears of fire and closed spaces, it seems she has been singled out for murder. With a full cast of suspects, it's up to Dr. Westlake to shine a spotlight on a killer--before it's curtains for Daphne Winters.