Just like assuming a hotel is pet-friendly, it can be a bad idea not to arrange for your pet to fly when you book your own tickets. The biggest hurdle you may encounter is a booked cargo area, and you'll either have to spend extra money to rearrange your flight schedule or choose to leave your pet behind.
You can try bringing your pet into the cabin with you, but some restrictions apply. Most airlines that allow pets in the passenger cabin require the pet carrier be small enough to be stowed under the seat in front of you. This doesn't mean you can cram your pet into any small carrier; airlines dictate your pet must be able to stand up and turn around inside [source: Probst].
Booking your pet's flight when you book your own can also help you avoid sticker shock at the ticket counter. Expect to pay almost as much for your pet's ticket as you paid for your own. For example, Delta Airlines currently charges $150 for a one-way, in-cabin flight for your pet. Expect to pay even more to stow your pet: One-way costs for checking your pet as baggage in the cargo hold is $275 for travel within the U.S. and $550 for flights outside the U.S. Keep in mind that these prices could change without notice [source: Delta Airlines].
If you can stomach leaving your companion in the company of strangers for a few hours, you may also want to check into pets-only flights, such as the ones offered on PetAirways. Putting your dog or cat on one of these flights might save you some money and, best of all, pets fly in the cabin rather than in the cargo area of the plane.