Problem is Hippo, so many of the places we've been to and checked out, well, we were dogless, so we could, and never took any notice of those rules and regs etc.
Mags is correct, Cataract Gorge in Launceston is fantastic, and the chairlift rides are simply stunning. Breathtaking really, particularly if you are afraid of heights like me! Lol. Just kidding.
Cradle Mountain is of course rather famous, and rightly so. Magnificent is the word to describe. Of course, where you go at Cradle very much depends on one's health and fitness level.
Now up near Smithton on the North West Coast are some great places to visit, but once again, don't think they are dog friendly.
I have a feeling that there could be more relaxed places (where dogs can go) on the East Coast, so perhaps check that out. Heck, you've simply got to see the East Coast anyway. It is the Paradise that the world hasn't discovered yet - can't rave about it enough. Not for those who thrive on city and fast paced things, the EC is just so laid back, as the scenery is just...well...photographers come from all over the world to photograph the EC, so I guess that says it all.
Tahune airwalk down towards Hobart is awesome, but once again, a major travel palce so possibly no dogs. They have a new Eagle skyride which is totally wicked. I haven't been on it, but by golly I want to!!!
It's such a peezy, tiny little state. I can get from one end to another in a bit more than what it used to take to go from home to the ruddy airport in Qld. You can go anywhere in such a bearable amount of time.
Sorry for the long post - obviously I love being here in Tasmania.