?Submissions to the International Genealogical Index (1992)/LDS reveal that the Dossett surname was in use in several counties in England in the 1500's:
London:John Dossett,1539, married Jone Hall Berkshire: Eline Dossett, 1542, married John Young Bedford:Robert Dossett,1543, born Surrey: Jone Dossett,1551, born Gloucester: Mergerat Dosset,1552, married Richard Symons Shropshire:Dorothy Dossett, 1557, born to John Dossett Buckingham: Roger Dosset,1563, born Hertford: Phillip Dossat, 1587, married Jone Franklyn
and that the surname was in use in the following English counties as early as follows:
Derby: Catherine Dossett, 1811, married John Green Devon:William Dossit, 1746, married Judith Bennit Dorset: Elezebeth Dosett, 1657, married John Burtt Hampshire: Elenor Dossett,1641, married Henry Fourd Hereford: Elizabeth Dosset,1768,married John Thompson Kent:John Dosset, 1642, married Elizabeth Bell Lancashire:James Dossett, 1852, born to William and Ann Dossett Oxford: Richard Dossett, 1641, married Joane Kirkham Somerset:Dorothy Dosset, 1607, married Edward Palmer Sussex: Benajmin Dossett, 1620, married Agnes Cybe
?One English author declared (or more likely guessed) that Dossett is "a corruption of Dorset.If not this, it must be baptismal, and be a corruption of Dowsett, which seems the more rational interpretation . . ."CHARLES WAREING BARDSLEY, A DICTIONARY OF ENGLISH AND WELSH SURNAMES (London, 1901, republished, Baltimore:Genealogical Publishing Co., Inc., 1980) at 249.