If my daughter was injured by a fire extinguisher box in the hallway of our apartment building, is there anything that I can do?

If your apartment complex has a fire extinguisher that has expired and or the law requires it be updated and the glass be changed to the glass that doesn't shatter or that it be updated by state law or building and safety code requirements and it hasn't been done, then the apartment owners and management could theoretically be held liable for the damages incurred by both children. As to hitting the head on the fire extinguisher box, if the children were being negligent in their play and they should not have been playing near such equipment and absent their negligent activity the box would not have broken and the glass would not have cut her, then it would be solely the chldren's fault and the court would not necessarily place liability on the apartment owner. You need to research more with the code requirements and you may wish to contact the fire department about the matter concerning codes.