I would agree with those who say to wait. There are many reasons - development of a puppy's bones, lack of discipline, etc.
Before you take a dog on their first hike, make sure they have basic commands down pat - sit, down, come, stay, heel, leave it, and so forth. It may save your dog's life.
Start preparing by getting the pup used to booties if possible. Work on commands daily.
Remember, only use your pup's name when the result is positive - pat on the head or small treat - and she will be more apt to come when called by that name. If you use it associated with punishment, she'll run away when called.
Get her used to noises, expose her to other animals where sensible - dog parks are good, cats if you have them, etc. Bunnies and squirrels can make a dog go astray.
Also, study the breed. Know her instinctual reactions to things. For example, we have Labradors. They will chase anything you throw. They are as attracted to water as a magnet to a fridge. Typically, they like to "scout" on the trail - they don't like to stay in "heel." They run ahead and then check back for direction. It's part of how they hunt. So knowing that, I trust Kenai off her leash, but I also know she'll listen if I call her. This has been tested on daily walks and occasionally, she has an "off" day where I keep her on lead because she's not listening.
I know that when other people or dogs approach or even horses, Kenai will listen and react the way I have trained her. But that only comes with practice and lots of trust built over a long time. I would not have trusted her like this when she was a puppy.
Sorry if that's long winded. Main thing is: Congrats on the puppy! Work hard and build a great bond and you'll have lots of great times! But keep each other safe!