If, by an injection kit, you mean injectable Solu-Cortef, by all means, YES, YOU SHOULD KEEP IT ON HAND!!!  Your doctor is WRONG.  I’m a non salt-wating 21-hydroxylase def. CAH adult male who has needed to inject himself when I’ve been stomach stick, severely dehydrated, or in shock.  If your daughter has an accident, EMTs will be VERY reluctant to inject her with cortisone.  Most people  -- even ER doctors -- do not understand anything about our disease.  As a parent, you must take direct responsibility for any possible situation.  While it is correct that non salt-wasters don’t have many of the concerns of salt-wasters, you still need to take precautions.  If your child goes into shock, or cannot take meds orally, she will get worse rapidly without the injection.  Better safe than sorry. 

I hope this helps.  Have a nice day.  Eric