One Dog and His Boy- Eva Ibbotson

Hal's parents refuse to consider a dog. Then they discover Easy Pets, a dog-rental agency. Terrier Fleck arrives on Hal's birthday, but when Hal discovers that his dog must be returned, he runs away. A large reward is offered for the missing boy, and soon they are being chased across the country. Helped by a travelling circus and sympathetic children from an orphanage, they race for their freedom.