"My dog died yesterday."
Translation:Вчера умерла моя собака.
Your word order is fine but with different emphasis.
"Вчера умерла моя собака.": the emphasis is on the dog's death:
"What happened???" - "My dog died yesterday."
"Моя собака вчера умерла.": you emphasize that you had a dog and the dog died yesterday:
"How is your dog?" - "He died yesterday."
There is also
- "Моя собака умерла вчера.": the emphasis is on the date of death:
"When did your dog die?" - "He died yesterday."
Because the English is neutral, I think that renordw's answer should still be accepted. As I think should вчера моя собака умерла.
I agree, you can't tell the emphasis from the English sentence, so why would one Russian version be more correct than another?
You did a fantastic job explaining the importance of word order in Russian. Leaving a comment here as a bookmark.