I don't think that's a low head set. The neck rises, she breaks at the poll so her nose is Almost vertical. In my book that's called a dogwalk. Next step would be working walk , then a flat walk with the horse nodding . If you get flopping ears, all the better. There's nothing wrong with that headset. There's a difference between TWH that show with higher steps and a higher neck set. Then there's the way the horse was meant to be. More of a low stepping , lowER neck set like yours and mine , for trail and (plantation, LOL), for covering distances at comfort to both horse and rider.
People outside this natural gait community are expecting what they see at shows with a high neck. They don't understand that TWH were specifically created for comfy long distance many years ago.
I belong to a barn that does not have show gaited horses. Just natural , no pads.
You can lift your hands to lift their neck and pick up speed and rack, but since a rack is inverted, it's not recommended for long periods.
I'm rambling, LOL.