We don't have a dog but we love them and have always had one in our younger years. With full-timing and the things we like to do, we didn't think a dog would fit in with our lifestyle.
No, you won't be able to take your dog into Denali and that's a must to do. However, there are probably kennels nearby. Also, the glacier cruises can last a full day. Would your dog be o.k. that long? The Fairbanks Riverboat Cruise also lasts a long time and we really enjoyed that, too.
If you're hiking with a dog and meet up with a bear, that could pose a problem as the bear could get agitated.
Otherwise, any other place would be easy to work around your dog. You will meet the same obstacles in the lower 48 with pets, especially in national parks and trails. However, many folks travel with dogs. I guess it just depends on how you want to sitesee, how long you want to leave your dog in the RV or if you want to put it in a kennel while you do so.
We get our dog fixes without owning one. It's a personal choice. Good luck!