I admit I'm a history geek so the history of small boat sailing fascinates me. There is very interesting thread on the history of planing boats over on the Woodenboat forum. Highly recommended reading if you would like to delve into the evolution of small boat sailing. A Mr. John Watkins, who seems to have a veritable treasure-trove of digitized historical material on his computer, provides most of the posts.
Older historical interpretations have Uffa Fox inventing the planing dinghy (International 14, Avenger, 1928) and this grew into the myth that Uffa invented the planing sailboat - all thoroughly debunked now. As you can see on the Woodenboat thread, candidates for first planing sailboats range from sharpies, to scows, to various rater classes of England, U.S., New Zealand and Canada. There are many different opinions championing several different design types. I've maintained that the first planing sailboats were the sailing canoes. They were light enough, the development of them as racing sail craft in the 1880's and 1890's was furious, and the sailors drove them very hard in the races.
Exhibit A - A photo from Outing Magazine, March 1891 (so this picture was taken in 1890). Lansing Quick getting the bow of his sailing canoe "Uno" up and going very fast offwind.