Lorraine, I haven't had much luck, but below are some records that I have been able to find.
It appears that Vincent was christened in St. Peters, Leeds ?
His marriage appears in the UK BMD...
Groom: DOBSON, Vincent
Bride: BROWNFOOT, Ana
Registration district: Leeds
County: Yorkshire
Year of registration: 1840
Quarter of registration: Apr-May-Jun
Volume no: 23
Page no: 320
Vincent & family in the English 1841 census...
DOBSON, Vincent M 20 1821 Coal Agent Yorkshire
DOBSON, Ana F 20 1821 Yorkshire
DOBSON, James M 1 1840 Yorkshire
Piece: 1343 Book/Folio: 5/10 Page: 12 Registration District: Leeds
Civil Parish: Leeds Municipal Borough: Leeds Address: Cross Green, Leeds
County: Yorkshire
Other possible approaches to find more data include work related information.
The 1834 Pigot's Directory of Professions & Trades in Leeds seems to indicate that Vincent may have worked with his father James at the time of the 1841 census...
"Fenton William, Waterloo Staith, East st -- James Dobson, agent"
Or maybe parish specific records may provide you with more luck...
Leeds also has a Tithe Map Project which aims to map the land ownership in the Leeds area during the early 1800s which may provide you with some clues about the extended family...
http://locateit.leeds.gov.uk/tithemaps/
To track these people down is an unenviable task as there were more than 50 Dobsons living in Leeds in 1841 that were born between 1785 and 1800!
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This MAY be Vincent's parents in the English 1841 census, but there are other christening records in the IGI where the wife is "Betty Marshall" so this may be a different couple.
DOBSON, James M 40 1801 Yorkshire
DOBSON, Betty F 40 1801 Yorkshire
DOBSON, Jane F 15 1826 Yorkshire
DOBSON, Elizabeth F 11 1830 Yorkshire
DOBSON, Emma F 5 1836 Yorkshire
DOBSON, Sarah F 3 1838 Yorkshire
Piece: 1301 Book/Folio: 3/23 Page: 10 Registration District: Todmorden
Civil Parish: Halifax Address: Slack, Halifax, Heptonstall County: Yorkshire
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Good luck.