Oh, Malling, I'm so sorry to hear that. It's awful to lose a pet at any age, but for her to go so young is heartbreaking.
As 1MM says, unless you've been in touch with the RSPCA, or there's anything written down in any papers from when you rehomed her, I don't think there's any reason to let them know; it's been a year; presumably any home checks etc they would do have long since ended.
Really sorry for your loss how awful for you. I think it's up to you whether you want to let them know. It's not like it's a breeder thst might need to know in case hereditary. Big hugs for you and your family. x
Sorry to hear your sad news. Post mortem doesn't bring them back, so it does seem an unnecessary expense. What breed was she? I think if you've had ongoing communication with the RSPCA then I'd let them know, but if they've not been in touch then it's up to you (unless there was anything in the papers to say that you should let them know). What breed was she? Any clues as to what it may have been.
We only had our rescue dog for 12 months when she suddenly died (age 2). I'm still in shock. I originally got her from the RSPCA. Should I let them know she died? We have already buried her. I did not have a post mortem due to the cost.