"My dog died last week."
先週、犬が亡くなりました was marked wrong. This is inconsistent in DL, because until now they accepted answers w/o the clear specification of the pronoun. Japanese rarely use pronouns and if you say 先週、犬が亡くなりました, it is implied that the dog was mine, if there is no context...
I agree, the pronoun isn't necessary. But I think using 亡くなる (nakunaru) is what is getting your answer marked incorrect. 1) It means "pass away" rather than "die", and 2) you wouldn't typically use it with an animal.
I guess the answer with 私 as a kanji just wasn't implemented yet. I reported it.