Gentle mommas are also good to use as a surrogate panel. Since she is new, just be careful. She may take offense and try to protect her baby.
Baby horses suck up every lesson you teach them, and every tme you handle them it is a lesson. Are you teaching good things or bad things? You are setting the foundation for this baby's entire life. You want good manners, a willing attitude, obedience and respect. Attitude can be influenced by breeding, but most of it comes from you. Ask yourself: do I know enough to teach? It is okay to say no. You find someone to teach you (hands on is best) and you learn.
What you are teaching is that if this baby backs away, the scary new thing goes away. The opposite of what you want. If it is not blind panic going away from you, just sliw backing, then that is okay, right now. Not what you want, but we have established the problem.
You said she follows and you can toich her with the halter. Can you touch her all over? Can you stand at her shoulder and scratch both sides of her nexk at once, or lay your arm over her? If not, this is what I would work on. You need to be able to move around her head, behind her ears, the bridlepath area, her face, her nose, her shoulder, her neck, her back.... so on and so forth. If she is comfortable with you there, move on with the halter and same thing. I don' start from the front to halter, I start from the side. Down and work my way up.
Caution. Baby horses are wild and dangerous. They are quicker, more flexible, and generally more reactive than older horses. Everything is new and scary, and they need a very knowledgeable hand to teach them. If you do not know enouh, there is no shame in getting hands on help. And that doesn't mean you won't be doing the work. BOY are babies a lot if work. Be careful. Go easy. Keep your lessons short(Their attention spans are only as big as they are). Do NOT get into fights with them. Be careful. Have fun.
And be careful.