When I inquired about piano or guitar for my first daughter most wouldn't consider her until 8 because
1. Maturity -many teachers do not know how or don't want to teach young children
2. Hand size and/or finger strength -young kids are sometimes not strong enough or don't have a wide enough finger span to reach notes for chords
My LO started piano lessons this past February about a week after she turned 4. She's been going to piano lessons with her older sister for over 3 years, so obviously she's been exposed for quite a while. She has great finger strength, good attention span and an interest so I felt she was ready. The teacher did a test lesson and recommended a shorter lesson of 15 minutes. I do not make her practice as it's exploratory and fun for her but even with just the weekly lesson, she is still progressing.
The program is called Simply Music. We attend teacher led lessons, but they do offer a home learning program. It does not initially teach kids to read music, but has a set of numbers/symbols that represent the hand placement. The thought behind it is to treat it how we learn language, so they learn to play first and read later. It has a sort of spiral approach as you go back to some of the songs (like Für Elise or Star Spangled Banner) a couple of times, learning additional parts and increasing in complexity, eventually moving to actually reading the music. I love the system and my older daughter (10) has steadily advanced in her skill sets.