Alar base reduction for 14 yr old girl; is it too young?

For females, surgery can be considered at 14-15 years of age if she has reached her adult height.  If she has yet to hit her growth spurt, or is still growing, then it is better to wait until she has reached her full height.  

I would wait for her to reach adulthood and sign her own consent. The face also develops and changes in form and shape as the child grows. A simple trim or alar base reduction may not suffice as this procedure will further pull down the nose tip. For a better outcome, the choice should be combination of augmentation rhinoplasty plus alar base reduction. 

Sorry to hear about your daughter being bullied.  Kids can be very cruel. I think at 14 she is probably a tad too young.  I would wait until she is about 15 or so when she has reached adult height and is no longer growing before considering any kind of nasal surgery.