All knee replacements are different...and don't be too discouraged (or encouraged) by what your surgeon says: he or she is only looking at the bone and incision healing and not much functional. This is not a dig at orthopods (well, kind of...) but just a result of their focus on the surgery itself.
I've rehabbed hundreds of knees in my career, and some are super fast and some super slow, most in between. I hope you have a good PT, and if not, then get one.
How is your range of motion??
Focus a great deal on two things in particular: your hips/butt muscles, and eccentric exercises for your quads (that's the lowering of yourself...like slowly lowering down a step). Tell your PT to focus on going down stairs...and you could start carrying a little bit of weight on your walks around your neighborhood. Yes you'll be tired and sore, but as long as its just tired and sore you're good.
As for when to take a trip? I'm assuming half day hikes would be possible? Start there and judge how well you're doing. If you can do 3 miles in your neighborhood now you should be ready for a short easy trip relatively soon. Take pain pills (!) and expect to be sore, but honestly, if you can do 3 miles in your 'hood now, once you can go downhill with more confidence you'll be ready to give it a try. Just be sure to ease into it.
Feel free to ask specific questions if you'd like...I don't mind a bit.
(Jenmitol AT gmail DOT com)