I don't remember ever seeing prohibitions for dogs, but you'd have to check to be sure.
It's a great hike. About 3 miles one way, and a very nice payoff at the end swimming in the pool at the base of the fall. Take a lunch and plenty of drinking water because it's a long, dry road to get there. It's pretty level the whole way, and therefore not bad to do with kids if they are good hikers (I've done it with mine, carrying my 2.5 year old, and my 5 year old got pretty tired).
Upper Calf Creek Falls I haven't done, but I want to. The hike is much shorter, but there is a big elevation change. It's much less crowded than the lower falls hike, but a friend who went there last year said it was a lot of fun.