I have no idea if any of these are the correct family or not but these are the only Hilda CARTERs that I could find bc1900 with father William in the 1901 census

1901
Victoria Street, Pinxton, Derbyshire
William CARTER head mar 32 colliery bank foreman b.Eastwood Nottinghamshire
Hannah wife 31 b.Hinxton Derbyshire
William son 6 b.Pinxton
Frederick son 4 b.Pinxton
Walter son 3 b.Pinxton
Hilda dau 3m b.Pinxton
RG13/3136 folio 112 page 11
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12 Ormiston Rd, Greenwich, Kent
William CARTER head mar 23 cannon? cartridge maker b.Socunder..bad? India
Hilda wife 21 b.Tatley? Oxford
Hilda dau 5m b.Greenwich
RG13/541 folio 182 page 18
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Wadhurst, Sussex
William Geo CARTER head mar 31 carter? on farm b.Woodham Ferris Essex
Agnes Eliza wife 33 b.Woodham Ferris
Ethel dau 6 b.Woodham Ferris
William John son 5 b.Woodham Ferris
Hilda dau 2 b.Woodham Ferris
Rg13/894 folio 7 page 6
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There were plenty of other Hilda CARTERs born about that time but all the others had a second name so I didn't check to see who their father was
Casalguidi