[Meela]

I'd be fine throughout the journey of the Fellowship. Moria might scare me to death, but with friends like those, who needs to fear? I'd just play the damsel act and hide behind Boromir's shield. And when in the midst of battle, it's easy to be inspired to join in with gusto.
After that, Amon Hen would be a piece of cake. And I could give some great pep talks.

I could never continue with Frodo and Sam. It's not the fear, I'd just lose my patience. Same scenery, same company, same lembas. A few days of those two moping on a volcano and I would have collapsed. Although Gollum might make good company.
Plus, the spider thing... I'd be in hysterics.

I'd join Aragorn, Legolas and Gimli. Helm's Deep wouldn't shake me too badly, I'd be in the spirit and fighting away. After that, it's just a question of getting through Pelennor - more room to get into a dodging position, or just to stand on the sidelines and wave your sword around occasionally. The Paths of the Dead would be almost enjoyable to me; I'm not afraid of death, ghosts, or the extremeness of the colour green.

If I was going to lose my nerve, it would be on Caradhras - heights and a fear of being buried under the snow and choking. The battles would be daunting, naturally, but once you're there it's easy to get in the mood. It's like going bungee jumping. You're terrified until you jump, then you get such a rush you want to do it all over again. Survive one battle, and you're attacking bushes for the thrill of it.

It's tempting to drop out after Amon Hen, but what do you do then? If you're stuck halfway through a journey, you might as well continue and see what's out there. I'd at least tag along until civilisation re-appeared. Once I reached Rohan, I'd have a clearer idea of the options facing me.
Thinking about it, I'd be more likely to back out at Moria. The thought of being trapped underground and attacked from all sides, even if it's not known when you first step in, is a tough challenge to face.

I could have handled the wilderness. If you're going with Aragorn et al, at least you end up with decent company and a horse. I would make it through Mordor through sheer endurance and some good pacing.