I'll check with my vet, but my instinct is he'll be fine, for what that's worth. I've done almost no exercise this year so he's only got to keep up with an unfit 42 year old lugging more stuff than he needs and a big camera and a tripod. He hasn't grown any taller for well over a month.
Not taking him isn't an option, only what we do while up there.

Things change so quickly on the mountains great great care should be taken don't mean to put a damper on your trip and I know you are thinking about your dog but I'd think twice my oh is a member of our local mountain rescue tea (30years)encountered some horrible sights both human and animal

If you are not doing long strenuous periods of exercise then that is fine. When someones says they are going up into the mountains, I think 6, 7, 8 hours day of hiking/climbing. Obviously this type of exercise is completely unsuitable for a growing puppy.

The long bones in the legs (etc) actually don't stop developing in large breed dogs until they are 18 months of age. So while physically on the outside the dog looks done growing, inside they are still in fact developing.