We had ours put down in August because of mixi too. He was the baby one and we still have the parents. Didnt realise we hadnt had him vaccinated feel guilty now. The children all understood that he had died but we have lost several cats and dogs already so they have experienced losing a pet before. Personally I would tell them. Mine were similar age when our cat was killed on the road there were tears but they soon recover and I just think its better to tell them what really happened.
Our rabbit 'ran away' when I was 3. I was just as upset as I would have been if my parents had told me the truth only it lasted a lot longer as I spent a couple of years hoping that she would come back and looking for her when we went to the park, to the woods etc.