Possibly the Kate Quilliam on Brian's birth index, who married George Shimmin in German on February 22 1891.
I do not see them in 1881, but in 1901 at 47 Dove Street Liverpool RG13/3439 folio 6 page 4.
George Shimmin Head 34 Corporation Labourer b Peel
Kate 33! b Peel
Edith May (?) 10 b Peel
William 8 b Peel
Margaret 6 b Cheshire
George 4 b Cheshire
Catherine 1 b Liverpool
Edith sister 21 b Peel