If the league has no rule regarding a player leaving the game under injury, then the umpire was correct in calling the first out. However, the umpire should have continued to call the out every time her spot was up to bat. I realize that this is just 12U, but the foresight falls on the league president to create this rule BEFORE the season starts. Otherwise, if there is no local rule beforehand, then it falls under the ASA rule, which says there is an out.
Out of curiosity, who protested the game, and under what grounds? The shorthanded team, or the winning team?