The GRO index mentions her birth as occasional copy  

EAMER, LILY  CHARLOTTE ELLEN    HOLLOWAY  
GRO Reference: 1903  March Quarter in EASTHAMPSTEAD  Volume 02C  Page 406  
Occasional Copy: B
also siblings
EAMER, FREDERICK  WILLIAM     HOLLOWAY  
GRO Reference: 1907  June Quarter in EASTHAMPSTEAD  Volume 02C  Page 433
EAMER, DOROTHY  VIOLET     HOLLOWAY  
GRO Reference: 1909  June Quarter in EASTHAMPSTEAD  Volume 02C  Page 415 
In Wokingham reg districtEAMER, WILLIAM  GEORGE     HOLLOWAY  
GRO Reference: 1911  June Quarter in WOKINGHAM  Volume 02C  Page 372
So they moved between the birth of Dorothy 1909 and William 1911