I measured the "Flea" and its string length is about 35mm (right about 13 inches). It would work with my hands as a mandolin, but would be a touch long for little fingers (IMHO).
I guess my big caution would be to spare no expense to do extremely ergonomic things with children. Accept no short-term discomfort... it can lead to long-term pain and life-long instrument aversion. Its hard to say, but from what you're describing, a 13-inch scale still seems too long to me. I would put substantially less weight on owning the same instrument into adulthood.
With its basis on the violin, the mandolin tuning really stretches out the left hand. Other plucked instruments by comparison can be played almost literally with one finger per fret. The Neapolitan mandolin tuning by its very nature has individual fingers covering multiple frets, and its doubled coursing and high tension mean that more force is required to fret the thing. If you're going for Neapolitan tuning, I'd opt for low tension and short string length. Thus my Cremonese/Brescian single gut/nylong strung recomendation. How to do that inexpensively, is something I don't yet understand...
"The effect is pretty at first... It is disquieting to find that there are nineteen people in England who can play the mandolin; and I sincerely hope the number may not increase."
- George Bernard Shaw, Times of London, December 12, 1893