I am looking for a book about a baby; it goes through one day. The baby loses his shoe and the puppy is caught with the shoelace in his mouth. There is a picture with the baby in a stroller, wearing a red cap.

Hi - I think you are looking for "Baby Looks", written by Esther Wilkin and illustrated by Eloise Wilkin. The Basset Hound has the babys shoelace in his mouth. It is a really adorable book.