Dax is so cute!
I haven't taken my cats out for some time now - my info may be out of date, but I can share my experience, and hopefully others here who walk their cats regularly can give you some tips.
It might be fun to take a trip to the woods as long as you're very careful, and take some precautions. A figure-8 or jacket harness is better for cats than a dog harness, which they can easily back out of.
I've taken Sylvestra out to a wooded park before in her figure-8 harness, and she loved it. I've also taken Felixia with me out to a park before, and she did well too. What I did for safety in both cases was to scout out the park to look for an area that was secluded and quiet, where it was unlikely that someone or something would come along and frighten the cat. I brought her in a her carrier with her harness on, attached her leash while she was still in the car, then carried her to the isolated spot in the closed carrier. When we got to the spot, I made sure she was calm & happy, then opened the carrier just enough to grasp the leash before unzipping the door all the way to let her out. I left the carrier open on the ground, so that if she got frightened she could head for it (a safe & secure known hiding place). And I watched her for any signs of fear so I could put her back in the carrier if she got frightened, before she became difficult to handle. Both cats are microchipped, and I also made sure they were wearing safety release collars with ID tags, just in case.
If Dax isn't used to a carrier yet, you'll probably want to get her comfortable with that first, so that if by any chance something did happen you'd know she would go into her carrier. Leaving the carrier out with the door open is a good start, and feeding her in it or giving her treats inside will help too.
Keep in mind that it's impossible to make any outdoors situation completely safe, but you can minimize the chances of problems if you prepare carefully.
Hope this helps