Actually, I have a monkey wrench on this one. I need a pet friendly resort that provides a shuttle.
Yup, that's going to limit your options a lot. I checked on hotels via Expedia and there are over 100 options. Once you check "Pets allowed", you only get 14 hotels. (I'm not familiar with any of those hotels, so I won't be much help here.)
But, here's some basic advice: While Disney resorts set prices and mostly sticks to them, rate at "regular" hotels will fluctuate much more. Whatever hotel you choose, make sure you have a cancelable reservation. Then, periodically check that hotel and others to see if you can find a better deal as your trip approaches.
Also, most hotels (including Disney resorts) require exact availability to make a change. So, be careful when making reservations if your trip dates aren't set in stone. If you have a reservation arriving on November 26th for 7 nights and your arrival date changes, you can't necessarily alter your arrival date to the 27th and stay for only 6 nights. Sometimes, it's smarter to make a single night reservation on either end of the trip with a longer reservation in the middle. Provided you book the same room type, you shouldn't need to switch rooms.
[I hope I explained that adequately. Ask if it's not clear.]
Finally, as someone who always stays at non-Disney hotels, I'd recommend setting aside a small sum to use for a few cab rides to/from your hotel from the parks. If your having too much fun (or feeling not so great) one day, it's great to have some funds set aside so you aren't chained to making the scheduled shuttles.