I've been giving lessons for over 4 years now, ages from 3-84, and I can safely say that yes, it is possible to teach really young kids, but don't expect anything until they get older. Avoid absolutely all theory, dont even bother with EADGBE, and all that. What instrument are you thinking of teaching to little kids? Guitar is horrible because you need a special sized guitar, they need to coordinate two hands since the very beginning, and you will overall be extremely frustrated. There was a parent who wanted me to teach their 5 yo kid guitar, and after me telling them that it was a bad idea, they wanted me to try anyways, so I did. Fast forward 6 months later, and Im hundreds of dollars richer, and the kid has nothing to show for those 6 months so I dropped him.
Piano is alot better, because you can play easy simple 1 finger tunes, then 2 finger tunes, then one hand tunes, and just progress from there. I have an 8 year old student who can play Rachmaninoff's Prelude in C minor, and his 7 year old brother struggles on the SIMPLIFIED Ave Maria, though they've been playing the same amount of time. It all depends on the kid's aptitude towards music really, but your teaching methods work wonders as well.
TLDR; Yes, you can teach students music, especially piano, at a very young age. Just keep it simple and avoid any and all theory.