Pets services and products are always in demand. If you check ads in places like Craigs List you'll see a lot of help wanted ads for dog walkers and doggie daycares. Pet businesses are hot right now, and predicted to get hotter. So, if you can think of a product, like pet treats, or a service (start your own dog walking service), you may have the beginnings of a home-based business.
There is a site that you can check out that makes dog and cat collars. They offer a kit to start your own collar business. I doubt that I would buy the kit, but the site is good to look through and get ideas. Brainstorm and research for a pet-related home business you can start. By next week, you could be in business with a pet oriented service or product. Good Luck!