This is the setup I used on my wife's small frame bike. It is made by Problem Solver and fits on most seat posts. There are some smaller rear racks made. I found one to put on our 4'11 tall daughter's 42 cm frame bike. This is the rack I used o my daughter's biek:
https://www.bikegallery.com/product/...k-367232-1.htm
Seatpost clamp__
https://problemsolversbike.com/produ...seatpost_clamp
This little guy can't be too much older than seven. He was touring with his mom in Denmark. He does nered to learn some pannier organization skills
I think his panniers are the same size Ortliebs that I use.
This setup is pretty common in Europe. Look at the hitch on the back of mom's bike holding her daughter's bike's front wheel. This allows her to tow the young lady when needed, and allows her daughter to ride when it is appropriate.