The ones that really stuck with my daughter at that age were Pippi Longstocking, Mrs. Piggle Wiggle, and Ramaona books. I wouldn't suggest Judy Moody. Mine is reading and loving those at 6, but she would have found them boring at 4. Same with Caddie Woodlawn (great book though). Others my daughter liked at that age included the Clementine books, The Doll Shop Downstairs, All of a Kind Family, Little House on the Big Woods (but not the whole series), Bad Kitty (graphic series--no girl protag.), Betsy-Tacy, Lulu and the Brontosaurus (kid is kind of a brat, but the story is fun)
Judy Moody is an "early chapter" book. In general I found early chapter books did not make good "read out loud" books. They are written to keep the lexile level down (difficulty of words) so they are easy for a emerging reader to read and don't really roll off the tongue well. Nor are the stories as rich and intricate, or as enjoyable to both parents & child. If you daughter isn't reading the early chapter books on her own yet, I would stick to picture books and regular chapter books and skip over early chapter books (Judy Moody, Magic Tree House) until they are ready to read the early chapter books on their own. You aren't missing much.
