Her service record would have been in her maiden and assuming that she was no younger than 18 when she joined up in 1942, that would put her year of birth around 1924 or earlier, that is to say, over 100 years ago. On that basis you may not need her death certificate. Have you found her in the 1939 Register? If her record is open, the change of name after she married is likely to be shown against her entry.
As Hugh says, speculating about where she might have been employed is not worthwhile until you have a few more solid facts about her. Does the photo of her in uniform show any rank or trade badges?