I took my little one on a buddy saddle behind me when she turned 4. By the time she was 5, she had developed her balance to the point she was flapping her arms and screaming WHEEEEEEEEEEE FASTER MOMMY, while we loped down the trail, at that point my trail companions told me she she was ready to navigate onto her own pony.
We put her in lessons and found her a 28 year old sweetie with cushings who she developed her skills on by following us on the trails for 2 years until the sad day came, and we were forced to find her next pony, purchased from her old lesson barn, and she further developed another 2 years on that one-that one is currently being free leased by a wonderful family with a 4 year old and doing lead line shows with her. Now at 10 my daughter rides better than most adults and many on this list can attest to that. her day will come if you are in a position to encourage it.
My little 20 month old granddaughter is doing the same thing, she's a natural horse person already - my horses instantly navigate towards her when she pops our of the SUV. I would NEVER put her on the back of a horse without me standing right by her side the entire time, and if i do it's on something i can for the most part, predict it's actions. when she is 4 and physically strong enough to stay in the buddy saddle, we'll do the same with her as i did with my daughter.