Dear Mr. Barton,
Thank you for posting your request on History Hub!
We suggest that you request a copy of your grandmother's Official Military Personnel File (OMPF). OMPFs and individual medical reports for those who served in the U.S. Armed Forces and who were separated from the service before 1959 are in the custody of NARA's National Personnel Records Center (NPRC) in St. Louis. In many cases where Army and Army Air Corps personnel records were destroyed in the 1973 fire, proof of service can be provided from other records such as morning reports, payrolls, and military orders, and a certificate of military service will be issued. Navy and Marine Corps OMPFs were not affected by the fire. Please complete a GSA Standard Form 180 and mail it to NARA's National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. Veterans and their next of kin also may use eVetRecs to request records. See eVetRecs Help for instructions. For more information see Official Military Personnel Files (OMPF), Archival Records Requests.
We hope this information is helpful, and best of luck with your family research!
Welcome to History Hub
You could go to the website fold3.com and get a 7 day free trial to search for your grandmother's military record.
Although I do not have a subscription I did see that Emma Harkey is listed on the website.
If you are willing to give her date of birth and area of residence they would help with searching for her information.
Here is some information on your grandmother below.
U.S., Department of Veterans Affairs BIRLS Death File, 1850-2010
Name: Emma Preston Harkey Birth Date: 2 Aug 1923 Death Date: 2 Jul 1993 Enlistment Branch: NAVY Enlistment Date: 12 Aug 1943 Discharge Date: 24 Aug 1945