Hi June,
Welcome to RootsChat.
Apologies if you know it already, but if you are searching in Dorset then you need to know this site:
The Dorset Online Parish Clerks (OPC):
http://www.dorset-opc.com It has a HUGE database and a good search engine.
I enterd "conway kinson" in the search engine with "Find ALL words" and got the following:
Parish of Kinson
1861 CENSUS
Schedule No; Location; Forename; SURNAME; Relationship; Marital Status; Age; Place of Birth; Reference
61; Constitution Hill; George Lockyer; CONWAY; Head; M; 35; Brickmaker employing 4 men; Kinson; ; RG9-1339F57p9
61; Constitution Hill; Martha; CONWAY; Wife; M; 27; Brickmakers Wife; Newfoundland; RG9-1339F57p9
61; Constitution Hill; Thomas John; CONWAY; Son; ; 6m; Brickmakers son; Kinson; ; RG9-1339F57p9
I like the fact, that at 6 months, son Thomas John already has an occupation !
I also found, on the same page:
77; For Holes; Mary; CONWAY; Head; W; 71; Brickmaker's Wife; Longfleet; ; RG9-1339F58p11
77; For Holes; Susan; CONWAY; Dau; U; 39; Dressmaker; Kinson; ; RG9-1339F58p11 Related, maybe ??
They also have the census for Lytchett Minster, with, lo and behold:
32, Wimborne Road, John , CONWAY, Head, M, 66, M, Tile & Brick Maker, Lytchett Minster, RG11/2097/F23p6
32, Wimborne Road, Charlotte , CONWAY, Wife, M, 66, F, Tile & Brick Maker Wife, Beaminster , RG11/2097/F23p6 All these brick makers !!! coincidence

related

Just a speculation, based on the age of the Lytchett John: could he be George Conway's dad, and the son is named Thomas
John after his granddad ?? Something to think about !
Another speculation: Lockyer is George's mother's maiden name

Regards,
Bob