(CBS) Many of us take our pets along when we go on vacation.

In fact, says the Travel Industry Association, some 29 million Americans bring their pets on vacation every year, and 76 percent of them travel by car. Of those, dogs are the most common (78 percent), and cats are a distant second, at 15 percent.

On The Early Show Tuesday, resident veterinarian Dr. Debbye Turner shared tips on keeping pets safe away from home, and spotlighted products designed to do it.

According to Turner:

To have a successful road trip with your pet, you must get your pet ready for the road.

The first and most important thing to do is to take your pet to your veterinarian for a thorough physical examination to make sure that she is healthy and ready for the stress of being away from home. If any of your travel includes flights, you will need a health certificate from your vet. Some hotels may require a health certificate, too.

Speaking of hotels, be sure to call ahead and confirm that Fido is welcome. Ask the hotel about any requirements or restrictions it has for pet visitors. That applies to friends and relatives you'll be visiting, as well. You don't want your pet to be "left out in the cold" when you reach your destination!

Also, be certain your pet has proper identification, such as a microchip or tattoo. Your pet should also be wearing a leash, collar, and identification tag with your name and phone number on it. Make sure the phone number is one where you can be reached while you're away, such as a cell phone number or a friend's number.

Finally, make sure your pet is used to the carrier and car BEFORE you take a long trip. Do short practice runs so the pet can get acclimated to the new environment.

You should also pack all the supplies you'll need for you pet, suich as portable food and water bowls, a leash, a collar with an i.d. tag, and a first aid kit (in case of emergencies or minor accidents). Also, take a full description of your pet and a current picture. This is important just in case your pet escapes, or is stolen. You'd have a ready description and photo to begin the process of looking for him.

It's important to have your dog on a leash AT ALL TIMES when out of the car. Small dogs and cats should always be kept in their carrier, to prevent escape. Traveling can be stressful for your pet and her instincts may cause her to run away just out of fear. Having him properly restrained would, of course, prevent that. Plus -- never let your dog run free at a rest stop or park: There a risk of them running into traffic and being hit by a car.

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