Yes, pretty much all the places are pet-friendly. There are hotels, B&Bs, the hostel and the chalet park which all take pets in at least some of their rooms / chalets.
Again, yes, there’s five pubs / hotels that you can take your dog into for bar meals. Some have areas outside as well where you can sit and enjoy a drink if the weather is nice. In addition, Spill the Beans café near Dunkeld Cathedral has a dog-friendly area.
Lots walk their dogs along the river path on the Birnam side. There’s also the recreation ground behind the GP surgery which is great for playing ball with your dog. Other nice walks include going up Birnam Glen, round the grounds of Dunkeld House Hotel, up Birnam Hill or through the Hermitage.
Sadly the local vet practice closed recently but there are practices in Pitlochry, Blairgowrie and Perth. Fair City Vets in Perth also provide an emergency service.
You can get some pet supplies at the village shop in Birnam and also at the Earn Equestrian shop in Dunkeld.
Normally along the river bank as I only have about an hour to spare at lunchtime. If I have longer I might do the Birnam Hill circuit or the Jubilee Bridge circuit, both of which take about two and a half hours.