On the Gateshead baptism, father Williams occupation is Tinner and Brazier, ie a Tinplate worker.
This will probably be them in 1841 census :
Easington Lane, Hetton le Hole.
William Stuart, 45, Tinner, b. Ireland.
Martha Stuart, 35, N (Not born in County)
Peter Stuart, 14, Y (Born in County)
William Stuart, 12, Y
Ann Stuart, 7, Y
Isaac Stuart, 4, Y
John Stuart, 2 months, Y
HO107/312/8/9/12
Next door is :
Isaac Stuart, 30, Tinner, b. Scotland
Jane Stuart, 35, b. Ireland
John Stuart, 13, N
Henry Stuart, 11, N
William Stuart, 8, Y
Thomas Stuart, 5, N
Eve Stuart, 2, Y
Jane Stuart, 3 months, Y
Next door again is :
Mary Stuart, 60, Ind., b. Ireland
Ann Stuart, 35, b. Ireland
John Stuart, 25, Tinner, Y
Mary Stuart, 25, b. Scotland.
No guarantee its your Peter, but it looks like this family originated in Ireland and made their way to Durham via Scotland and Northumberland.
Alan.