Juliet recommends Little Bear's Friend by Else Holmelund Minarik.
This may be an old book (now out of print?) but it is a beautiful story about friendship, perfect for emerging readers. It has lovely illustrations by Maurice Sendak, simple vocabulary and sentence structures, and is broken into shorter chapters, so is not too daunting. There are other stories in the series, but this is my favourite!
Recommended for Under 4's.