As for children traveling within the U.S., there are no 'kiddie discounts'; they are treated like adults when it comes to base ticket prices, with one exception: children under the age of 2 can sit on a parent or guardian's lap for free (but be prepared to prove your tyke's age). If you want to buy an under-two year old his or her own seat (which the FAA recommends as a safety measure), you will pay the same as the grown-up seats. However humans do have one edge over pets because people can take advantage of airfare sales and specials. There are no such deals for Fido.
Are pets and children ever banned from flying?
Absolutely. US Airways doesn't accept animals in cargo while Virgin America's cabin pets can't travel in first class. Delta bans pets in cabins and cargo but only on its 767s. Hawaiian allows pets in cabins but not on flights from the U.S. to Hawaii (with the exception of service animals). To top it off, several airlines restrict short-snouted breeds in cargo during extreme weather but United refuses to transport adult English bulldogs "older than six months and/or weighing more than 20 pounds at any time of year," according to its web site.
For children, it's a little easier: All U.S. airlines accept kids but should you happen to find yourself in first class on Malaysia Airlines, look for your child in coach. That's right, no little ones are allowed in that carrier's elite seats and reaction seems about evenly divided between anger and ecstasy.
Advantage? I'd call this a draw.
Animals and kids are known to be excitable and on rare occasions, pets run away and sometimes get lost. Fortunately, when toddlers go charging down the aisle, they are invariably recaptured.
As for the owners of Beauty-the-mutt, none of this matters since they'd never get her to an airport in the first place. "She can't stand car rides," they said.