treading - referrals are no big deal, they are the proper, accepted way forward when something presents which is out of the ordinary and beyond the scope of the GP. From what you have said about the GP you saw, I don't see how you can have confidence in her reading of the situation and her response. She may be right, but the point is she's not an expert, she hasn't dealt with the situation in a way that alleviates your worries or fully answers your questions, and a referral to a specialist is the correct and sensible way forward in this instance. You are absolutely NOT wasting anyone's time, and don't take any notice if you feel that that is being implied to you by the GP or the practice.
There may be a simple diagnosis here, or it may be something more complicated which will affect your daughter and you as a family and will need experts to manage it. The point is, at the moment you do not know which it is, and you owe it to your little girl (as well as yourself and the rest of your family) to make sure that it is dealt with as promptly and effectively as possible. Good luck - and if they say no initially for any reason, just find your inner tiger mother and insist.