If she will follow you without being headcollared, then just do it and attach the lead and start wandering around, keeping within her comfort zone/near her Momma/in an area where she is used to following. In the earlier times with our little ones we simply used to thread a piece of string through the head collar and hold both ends before walking forward - if someone had a hissy fit then we could just slip the string and they were free. Not what many folks would suggest today, mostly they say hang on and dont let go, but I have always worried about injuring a foals neck bones by 'hanging on', and they never ran off once free, leaving us to re-approach, give scratches and try again. Never took more than a couple of 'leading' sessions for them to catch on! Nowadays we follow the playtime route with all the 'work' done before they ever start wearing a headcollar.
No, never tie up until they are leading confidently and for quite some time/and in different places/circumstances. Our tying up times can come several months later as we rarely find the need to tie If the leading is done properly and confidently and the little one knows all about ropes being 'obeyed' and not something to fight, then tying is a natural progression. At first I would simply wrap the rope round a smooth solid surface - like a gate. Keep hold of the end and give a short groom or similar, do not let the rope go, but you can give and take on it if this first 'tie' causes a bit of shifting about. Next tie, obviously with a quick release, to a thin piece of string or something that will break should there be an emergency, but seriously, if you have done your leading correctly then there should be no problem with tying, just make sure that the rope is at the right height, not low enough to get a foot over and not too tight. We usually tie ours for the first time when trimming their feet as they are used to this happening, and none of them have ever been any trouble. But neither do we leave them alone when tied until they are a lot older, even then only if we have to quickly fetch something, we do not follow the idea of tying and leaving them alone " because it is good for them/because it teaches them good manners/they need to learn a lesson for some reason"????? As the years go by, ours will stand for as long as we want simply because they are happy and confident enough to do so!
So just continue with what you are doing, take it slow - what's the rush anyway! You will be fine.