Here's the deal, do NOT leave a burner full of hot or boiling wort with a dog around. I mean, that's just common sense. So much can go wrong and cause the dog serious or fatal harm. So, my advice is either be present the whole time or do not leave the dog outside with an unattended burner/kettle. Removing the dog from the equation, once you are past hot break and have added the hops there's very little chance of a boil over. That's mainly a risk when coming to a boil, during hotbreak formation, and hop additions. I've stepped away to use the bathroom and such but personally I prefer to not leave the boil unattended for more than a brief moment. Other things that can happen is the wind can blow out your flame - happens all the time in windy'ish weather (which for me was always spring/fall primarily but can happen at any time). Things can also fall into the beer such as tree leaves or anything that can go airborne like a plastic bag.
So, my advice is no... don't leave it unattended for 10-15 minutes or more straight and definitely don't ever leave the dog alone with it.
Rev.