Universal Prekindergarten and Early Childhood Education Act of 2011 - Amends the Elementary and Secondary Education Act of 1965 to allow local educational agencies (LEAs) that receive funds for 21st Century Community Learning Center activities to use them also for educational activities for children four years of age or younger, if the LEA agrees to phase in, where possible, a prekindergarten program taught by teachers with qualifications equivalent or similar to those teaching other grades in the school involved.