I had looked at this one about 3-4 years ago but got stuck. Now relooked at it and still stuck on a few things but more positive on others. I agree with Frances on who likely are her parents. My notes follow:
Likely matches baptism of Matilda Killey 29 May 1831 Malew IOM, d/o Edwd Killey & Jane Corrin.
FS Baptism Image Malew 1831: "Matilda (illeg't) D of Edw'd Killey & Jane Corrin 1831 May 29".
She is Matilda Brew in 1841 census probably because her mother married John Brew in 1839:
1841 census at Back Bond St, Douglas, Parish of Onchan 1465 33 8 pg 24
John BREW 35 Labourer Yes
Jane BREW 34 Yes
Matilda BREW 10 Yes
John BREW 1 Yes
1851 census at 12 Stanley Terrace, Conchan 2525 37 pg 25 #88
Matilda KILLEY, Servt 20 House Servant, b Douglas I of Man
at home of Martha Andrews, Widow 56 House Propr b Ireland & family
She left the IOM sometime after 1851 because she is in Yorkshire in 1861.
1861 census at 5 Camden Terrace, Bradford Reg Distr, Manningham Civil Parish, St Jude Ecclesiastical Parish, Yorkshire 3333 76 pg 35 #177
Matilda KILLEY, Servant Un 27 Cook Domestic Servant, b Isle of Man
at home of Samuel Bergel 43 "Yarn & Stuff Merchant" b Hamburg Germany
Sometime after the 1861 census she started having a family, presumably with a Thomas Gellen or Gelling because his name was given as father when the two eldest children married.
1871 census at Sodhouse Green, Ovenden, Halifax Yorks 4419 25 pg 12 #51
Matilda KILLY, Head Unm 36 Housekeeper, b Isle of Man
William G KILLY, Son 8 Scholar, b Yorkshire Ovenden
Mary A KILLY, Daur 6 Scholar, b Yorkshire Ovenden
1881 census at 36 Brickfield, Ovenden, Yorks (W Riding) 4420 44 pg 19 #104
Matilda KILLEY, Head Widow 43 House Keeper at Home, b Isle of Man
William KILLEY, Son Unm 18 Cutter Dye Works, b Ovenden Yorks
Mary Alice KILLEY, Daur Unm 16 Worsted Livister, b Ovenden Yorks
Frank KILLEY, Son 9 Scholar, b Ovenden Yorks
Martha J KILLEY, Daur 4, b Ovenden Yorks
The family must have moved to Douglas IOM after the 1881 census because her two eldest children married there in 1886 and 1887 and Matilda died there in 1886.
FS Burial Image Braddan 1886: No 3967 "Matilda Gellen, Douglas, 1886 July 2, 57, Frank Tibbits Curate"