Always do what is best for your pet. If air travel is involved, then leaving pets at home with a good pet sitter is usually the preferred option. When you do travel with your pet, deciding what to take is always a  petessentials   good place to start. Depending on the mode of travel and the length of the trip, you will need to pack any necessary medications and medical records, especially if your pet has chronic health problems or is currently under a veterinarian's care for an ailment. And the appropriate paperwork is essential if your travels take you across international borders (see the links below for specific requirements).

Then you will need the basics like food, food/water bowl, pet first aid kit, bed, leash, collar, required tags (ID and rabies), grooming tools if your dog requires regular grooming, pet waste bags, crate, and toys (especially an interactive or chew toy that will keep them entertained). You will also need litter and a litter tray or disposable litter trays for your cat. Just in case, take a recent photograph along. It will be much easier to locate your pet if it becomes separated from the family if you have a photo to show people. And if your pet has an embedded ID chip you will need to have the phone number of the company and your account details so you can immediately contact them.

Your pet should have its own bag so you know where everything is and can grab items when you need them. Don't forget to carry some water if traveling by car, and remember to take enough of your dog's regular food for the entire trip. If you can't find the same brand on the road, abruptly changing a dog's diet can cause stomach upset and diarrhea, something to be avoided while traveling. It is always best to stick to their regular feeding schedule as well.