I recently read this with my advanced 5yo daughter. While she liked the book, and found it readable and easy to follow -the abridged version we read doesn't have many complicated metaphors or inferred settings- I was quite surprised by the emphasis on death and neglect in the book.
It opens plainly stating that the main character, Mary, is not wanted by either of her parents. That cheery note is immediately followed by Mary's entire household dying from what I assume to be cholera or the like, while the little girl spends at least a day, likely more, alone in a room. She is subsequently shipped off to two households of strangers, and finally meets a boy of her age who spends a lot of time talking about not growing up, having a fatal illness, his mother's death, and how his father doesn't like him.
All that said, my daughter didn't seem phased by these details and happily finished the book. My guess is that she is too young to fully process the implications and nature of neglect, parental abandonment, and untimely death. I do, however, have friends whose young children would have nightmares, anxiety, and ask endless questions about death if they were introduced to this book too early. If you are thinking of reading this to your young child, and you know they are sensitive, I would encourage you to read the book ahead first. I have also heard that different editions of this book are more specific than others about the darker parts of this book, so you may be able to find a more child friendly version than I have.