Every country in the world has their own rules. Quarantine is to be avoided only with proper papers and
documentation. For
dogs it would need to be 30 days if you had to go through Quarantine as that is how long they wait to determine if an animal has rabies. Even with all the shots and paperwork if you take an animal ashore without clearing
customs you are in trouble and could lose your pet as well. That is pretty much true every place that chooses to enforce the law. How well it is enforced is another matter. You may have no incidents and never attract attension but if you did then it is suddenly a serious matter. Local police may ignore you but a
customs official won't. With the worldwide concern over the spread of disease it can be more serious in places that never used to care.
Every country at every port entry has to be handled each in turn. That includes coming back home too! The fact your dog was out of your home country matters when you come home. I'm sorry I don't have all the particulars for the places you might go but you do need to treat each country as a new set of rules each time you enter or re-enter the country.