magic !

Name: Lillian M Dawson
Year of Registration: 1912
Quarter of Registration: Oct-Nov-Dec
Mother's Maiden Name: Badham
District: Ross
County: Gloucestershire, Herefordshire, Hereford and Worcester
Volume: 6a
Page: 783

So Elsie "fell" sometime Xmas / winter 1911-1912, 10 months earlier she is
in the 1911 Census (Sunday 2nd April) she is a Cook in Dorney Wood, Burnham ( nr Slough). Other male DAWSON's in the area include :-

1911
DAWSON ALBERT L M 1899 12 Eton Buckinghamshire
DAWSON ANDREW M 1874 37 Eton Buckinghamshire
DAWSON AUGUSTINE RAWKINS M 1847 64 Eton Buckinghamshire
DAWSON HENRY M 1865 46 Eton Buckinghamshire
DAWSON HORACE M 1871 40 Eton Buckinghamshire
DAWSON LIONEL A M 1899 12 Eton Buckinghamshire
DAWSON CALEB W M 1871 40 Windsor Berkshire
DAWSON THOMAS WILLIAM M 1879 32 Windsor Berkshire
DAWSON WILLIAM JAMES M 1879 32 Windsor Berkshire

I'd still keep an open mind to a marriage -somewhere maybe not in England or Wales.

Again I'd still not rule out a WW1 death for Mr DAWSON, a possible given the condition of Widow when Elsie marries Mr GALE in 1915.