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
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
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!
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