At our library story time in Kansas I loved when this book* came up in the librarian's rotation. I don't remember if the librarian told this story with a flannel board set-up... but I remember we visually worked our way through all the spots the dog acquired throughout the day. Very fun.
At a recent trip to our (sub par**) Virginia library we picked up this book by the same author. Also very cute about a girl who describes all the types of funny dogs she doesn't want and that she just wants a dog she "can call MY DOG!"
Here are some other dog books we love in our house (since we all love the idea of dogs and the kids desperately want one tomorrow). And Buddy and Baby X are fairly obsessed at the time with dogs.
Doggies by Sandra Boynton has been a favorite board book among all our babies.
I'm sure you've all read, or at least heard of Harry the Dirty Dog.
And my childhood favorite: Part-Time Dog. (I'm fairly certain that the above and linked to version of this book are updated versions of the one I read as a kid.)
And you can't forget the McDuff series by Rosemary Wells. I LOVE these books.
*I usually use book images from Amazon.com and link you to the book page at Amazon so I don't get in trouble for using their images. But also because I buy probably 90% of my books from Amazon. Books are usually 30% off online, and if I spend $25 (which isn't hard for my family to spend on books) there is free shipping. Otherwise, I am a member (free membership) of Borders Rewards and I print out their coupons that get emailed to me and purchase the books at Borders.