C.W.
They should take her to an ear, nose and throat doctor. My friend's 4 year old always had breathing problems and it took years to figure out what was wrong (tonsils and one other glad near the ear). The ear, nose and throat doctor knew right away what was wrong and how to fix it. It's best to get it checked by a specialist as early as possible to avoid any avoidable health and/or associated behavioral problems.
Good luck!