I know I'll get heat for this, but I'll put it out there for consideration, anyway.
Is your cat sick? Even a healthy cat can have digestive problems when moving around from place to place - but if your cat is ill, this might be more of a problem than you realize. You don't want to have to run around looking for a vet, medicine, etc.
I have taken a dog and cat when I moved from the US to Paris - but I would never do it again, because it's too stressful, both for the animal and the owner.
When I travel with my little dog, she must remain cooped up in a carrier on the train, bus or Metro, and is not at all happy about that. Animals require a separate paid ticket on trains.
Most hotels ask you to keep your companion in the carrier if you leave your room, for insurance and security purposes. I assume you have checked to see that cats are allowed? Many hotels will allow dogs, but not cats, because of allergy problems and litter boxes.
Animals are generally not allowed in stores, even when in carrier bags. This means that you'll be leaving your cat alone in the carrier in the hotel, if you want to go see the sights. Dogs are allowed in many cafes and some restaurants, but I've never seen any cats.
It's obvious that you care for your cat, and would rather not leave her behind. But all things considered, it doesn't sound like much fun for her - and probably not you, either.
You might be doing your cat a big favor if you could find someone reliable to babysit her while you are away. Even though it's a long time, your cat won't actually know the difference and will just be glad to see you when you get back. Plus, you won't have to deal with the food problem.