McKay, Scott and Whatmore all claim that COLONEL QUARITCH, V.C. was first published as a serialized novel by Harper & Brothers beginning July 7, 1888 in HARPER'S WEEKLY, and it contains an unknown number of illustrations.
McKay, Scott and Whatmore claim that it was first published in London in 3 volumes (triple-decker) by Longmans, Green and Co. on December 3, 1888, and that 3,000 copies were printed. Longmans also published a 1-volume edition in 1889.
Harper & Brothers published its authorized first American edition in 1889 in New York. This edition is illustrated with 4 plates, originally found in the serialization of this novel by the same publisher.
In 1890 Longmans published a new edition with a frontispiece, and a title-page vignette.
Circa 1906 George Newnes published in London an edition with 8 illustrations by Cyrus Cuneo.
See the VisualHaggard.org page dedicated to the illustrations found in various editions.
I do not own any of the books pictured, unless noted.