Rubbish! My guess is that she lived and died in S Africa so that the Anne H. deaths on FreeBMD are none of them hers.

No birth found in Scots records or in FamilySearch,

In fact she is found in the 1881 census in Abbotsham, Devon:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year  Occupation  Birth place

Annie Hamilton Head Widow Female 40 1841  Officers Widow  Scotland
Mary Hamilton Daughter Single Female 5 1876  Scholar  India
Ranald Quickshaw Cousin Single Male 5 1876  Scholar  India
Clara Mitchell Servant Single Female 16 1865  Cook (Domestic Serv)  Bideford, Devon

Address & Ref:

Street Buckley Villa
Parish Abbotsham
County Devon
Archive reference RG11
Piece number 2260
Folio 6
Page 5

  RG11, Piece 2260, Folio 6, p. 5
________________

Even more in fact she is found in the 1891 census in Abbotsham, Devon with her youngest two daughters and a host of young relations:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year  Occupation  Birth place

Annie Hamilton Head Widow Female 51  1840  Living On Own Means  Scotland
Ethel Hamilton Daughter Single Female 22  1869  -  New Zealand
Mary Hamilton Daughter Single Female 15  1876  -  Abbotsham, Devon
Broughton Hawley Nephew Married Male   14  1877  -  Italy
Ronald Cruickshank Cousin Married Male 15  1876  -  East Indies
Harold Cruickshank Cousin Married Male 14  1877  - East Indies
Eustace Cruickshank Cousin - Male 8   1883  -  -  
Susan Ford Servant Single Female 22  1869  Domestic Servant Cook  Devon
Ellen Beer Servant Single Female 23  1868  Domestic Servant Housemaid  Devon

The married staus of the relations is on the form but obviously wrong!

Address & Ref:

Street Buckleigh
Town Abbotsham
County Devon
Archive reference RG12
Piece number 1787
Folio 4
Page 2

   RG12, Piece 1787, Folio 4, p. 2
________________

She is named in the 1881, 1891 aand 1901 censuses as ‘Annie’ Hamilton.  Her birth was given as 1841, 1840 and 1832.  A search for her death in 1906 +/- 1 year and with a birth in 1837 +/- 5 years, gives precisely one candidate death index:

First name(s) ANNIE
Last name HAMILTON
Gender Female
Birth year 1833
Age 73
Death quarter 4
Death year 1906
District Guildford
County Surrey
Volume 2A
Page 62
Country England
Record set England & Wales Deaths 1837-2007
__________________

Her probate index:

HAMILTON Annie of “Broadview” Pirbright Surrey widow died 13 November 1906  Administration London 15 February to Mabel Hamilton and Ethel Katherine Hamilton spinsters  Effects £2945 17s. 6d.
______________

Their marriage transcript;

First name(s) Thomas Rice
Last name Hamilton
Marriage year 1853
Marriage date 21 Apr 1853
Spouse's first name Anne
Spouse's last name Baumback
Presidency Bombay
Groom's father's first name John
Groom's father's last name Hamilton
Bride's father's first name George
Bride's father's last name Baumback
Catalogue description Parish register transcripts from the Presidency of Bombay, 1709-1948, :
Archive reference N-3-27
Folio number 128
Record set British India Office Marriages
_________________

The image provides the additional data:

His job: Lieutenant in H.M. 8th Regt.
Place:   Malcolm Peth
Residences: Both living in Malcolm Peth
Banns of Lic: By Licence
Witnesses: J R Hadow, M C Holmes Captn, Pauline Pawell, Adselaide Andrew
__________________