I haven't actually done it but did a lot of research last year on this subject....oddly right around this time. I figured that I would need to take the dog down to visit my DD at some point while she was away working. Didn't end up happening but might this winter. Anyway, the biggest issue for me is the airline rules. The dog would have to be able to fit in, an approved, carrier under the seat and must stay there for the duration of the flight. While my dog barely meets the weight limit I am not certain that she would fit under the seat. She's kind of an odd shape.....think along the lines of a Corgi. There is no way I would take her flying in cargo. You do have to book in advance and there is a limit to the number of animals on a flight. The pet carrier counts as your carry on. You are only allowed a personal item and that is subject to gate checking....I honestly don't see them actually gate checking it though unless you had a giant backpack. Other things like vaccinations and documentation is not a big deal. I did wonder if there were issues with rental cars but never looked into that. Hotels are super easy to find ones that allow pets. One thing to note about hotels is that they have rules about whether or not you can leave the pets unattended...some do not allow it at all. They always charge a fee, some a flat fee and others are a nightly fee. Many require a large credit card hold to cover any possible clean up.
ETA...different airlines have different rules. They are all pretty similar but the main variable I found was the weight limit.
