I am so sorry for your loss.
My son's classmate was also 4 when her Dad passed earlier this year. He died at home, in his sleep, from a heart attack. The doctor told her Mom not to tell her that he was sick and not to tell her that he died in his sleep. Reason being, when the girl would become sick or go to sleep (or when anyone close to her as well) he said she may think she would/they would die like her Dad. They ended up telling her that something in Daddy was broken and that he went to Heaven. They also told her that even though Daddy was no longer here, that he loved her very much.