Hi,

I searched for her death in Ancestry and FamilySearch and Alpena Death Records 1905 to 1995 from the Alpena newspapers but didn't find her death in Michigan.

Anna Plunkett
Died: 25 June 1891, Brown Co., WI
Source: Vol. 2, p. 0120, reel 005, Wisconsin Vital Records Death Index 1820-1907.

You'll want to get an obituary to verify this is your Anna. Successful Searching!