Horses are herd animals ... going out alone somewhere unfamiliar only provokes the instincts and they will act to protect themselves ; I don't think your horse is trying to behave badly, only looking for leadership. If you hesitate even for a moment, they will take over and try to lead themselves. So, if you get anxious, your horse knows it, and will take it upon herself to keep herself safe (which is where the anxious/alert behavior surfaces). The horses that are fine on the trail alone are the ones that don't mind being the leader. Some horses just aren't like that. Just be calm and don't EXPECT anything to go wrong - never get on a horse and expect it to do something bad, even if they do it every single time you ride. Get on and expect it to be the best behaved horse in the world and when something arises, correct it the best you can. Be prepared, but not expectant... if that makes sense.
Let her use her feelers and observe what's around her at her own pace; don't rush her or ask her for things she isn't ready for.
Also, if you want to "practice", go out with another horse in a single file line and keep your horse up front (don't pass sides). See how she acts. Is she equally alert and anxious, or is she more calm with another horse there? If she is anxious, move her behind the other horse and see if she relaxes. If she's not, the problem is the rider.