What better gift idea for a child than dog toys? There are plenty of them, for all ages, from babies to bigger kids.
Of course, you can choose a dog that also sings a lullaby - I have seen they have lots of positive reviews.
Some of the plush toys are made to look like a specific breed - see for yourselves. But I have to warn you that the choice is tough, they are soooo cute! And I guess many grow ups would like this kind of dog toys, too!
You might go with a classical toy as a slinky dog - but be aware that it is appropriate for older children.
For children who can't have a dog (because they are too young or because they are allergic), a nice alternative are the FurReal dogs.
Another idea, for those who love board games: dog monopoly! There are generic ones or monopoly for the lovers of a certain race.