From what it looks like (If it's the correct Annie), Annie never married, worked as a midwife & died as a spinster.
There was a Annie Louisa DOWSON born in 1872 in New Zealand.
There was also a Annie Jane DOWSON born in 1880 in Christchurn, NZ.
________________
Annie Louisa DOWSON, B:1872 in NZ
Parents were: Emily Annie & Thomas William DOWSON.
Children of Emily & Thomas were (There could be more):
1867 - Elizabeth Emma DOWSON (Died 1945 - buried at Te Aroha, Cemetery)
1867 - Emily Sarah DOWSON
1869 - Melvin Turner DOWSON
1870 - George DOWSON ??
1872 - Annie Louisa DOWSON
1872 - Egbert John DOWSON (Died 9 Feb 1920 in the Boer War)
1877 - Wilfid Cuitt Chilve DOWSON
Parents, Emily died in 1925 at Kaiaka, & Thomas in 1912
________________________________________________________________
1905 - NZ Electoral Roll
Name: William Romaine DOWSON - nurse/settler
Kaiwaka, Marsden, Northland, N.Z
Name: Annie Louisa DOWSON - Spinster
Maungaturoto, Northland, N.Z
_____________________________________________________________
1911 & 1914 - NZ Electoral Roll
Name: Thomas William DOWSON - farmer
Name: Emily Annie DOWSON - married
Name: Elizabeth Emma DOWSON - Spinster
Kaiwaka, Kaipara, Northland, N.Z
Name: Annie Louisa DOWSON - Spinster
Tatarariki, Kaipara, Northland, N.Z
_____________________________________________________________
NZ Gazette Entries
Name: DOWSON Annie L Miss
Date: 1916 & 1917
Place: Northern Wairoa
Occupation: Midwife
Source: NZ Gazette 1917
Page: 1370
Record Type: Midwives Register
_____________________________________________________________
1919 - NZ Electoral Roll
Name: Emily Annie DOWSON - Widow
Name: Elizabeth Emma DOWSON - Spinster
Kaiwaka, Kaipara, Northland, N.Z
Name: Annie Louisa DOWSON - Spinster
Tatarariki, Kaipara, Northland, N.Z
_____________________________________________________________
1928, 1935 - NZ Electoral Roll
Name: Elizabeth Emma DOWSON - Spinster
Kaiwaka, Kaipara, Northland, N.Z
Name: Annie Louisa DOWSON - Spinster
Kirikopuni, Kaipara, Northland, N.Z
_____________________________________________________________
1938 - NZ Electoral Roll
Name: Elizabeth Emma DOWSON - Spinster
Name: Annie Louisa DOWSON - Spinster
Kirikopuni, Kaipara, Northland, N.Z
____________________________________________________________
Annie Louisa DOWSON died 17 March 1939 & looks like she never married.
Attached is a photo of Annie, as there are people with Annie on there family tree.
http://trees.ancestry.com/tree/5061199/person/5082181881