Will my child be disqualified for a false start?

Not for the first one. UKA Rule TR16 S2 gives Under 14s and Under 16s (and everyone in Open Graded races that U14s or U16s may enter) a warning first:

• Individual races: a first false start earns a warning (yellow and black card). A second false start by the same athlete means disqualification (red and black card).
• Combined events (such as pentathlon): disqualification only on a third false start by the same athlete.

This is more lenient than the senior rule, where any athlete responsible for a false start is disqualified straight away.

A false start means starting after taking the final set position but before the gun: in a crouch start, a hand or foot losing contact with the ground or blocks; in a standing start, a foot losing contact with the ground.