There is a whole collection of children's stories dealing with cats and dogs, some that come to my mind right now is the Two Gray Cats series, Paw Island, there is the Rottwieler that talks, oh there are a lot.I just can't think of any right now off the top of my head. My suggestion to you is to join an online writers club. They are free at about.com you have to register but again it is free and then you figure out for yourself which writers forum you would like to be in. They have what they call a Daily Prompt, where they just put a statement out there, like "Love comes from the heart" what does that mean to you- and then you go off on it and write, and then submit it to their boards and people critique you and help you to develop your style.
Another suggestion is to start going to book sales and pick up children's books and read them and gain ideas about them. You can buy for about $35.00 at a regular bookstore, a book called The Writer's Market and inside you will find lists and lists of magazines, periodicals, publishers, and their critieria for what they are looking for and how to submit your work to them.