Yes, it is generally allowed to hike through the Wimbachklamm with dogs.  However, there is a leash obligation - even before the gorge.  In the area between the Wimbachbrücke car park and the gorge there are meadows where sheep graze.  Therefore, there is also a leash obligation here.  There is no entrance fee for the dog.  He can enter the Wimbachklamm through the dog slit next to the rotating grate at the bottom right.  Make sure that the leash is short in the gorge so that other visitors are not harassed by your dog.