Hi Tracy,
A two-week stay at
Disney's Old Key West Resort sounds positively wonderful! I love this resort for the extremely relaxing Florida Keys feeling, and two weeks there will give you lots of time to sink into the resort. Although I know you are looking for quick-service dining, if you have the time one day, do give Olivia's Cafe at your resort a try. I find this restaurant offering down-home Florida fare to be a hidden gem!
You are welcome to dine at any of the quick-service locations throughout Walt Disney World; you do not have to stay just with your resort. My recommendation for where you look for other quick-service dining will depend on if you have a car, or if you are willing to spend a bit of money on a taxi. Getting from resort hotel to resort hotel, even if they are geographically close, often requires two modes of Disney transportation as you often need to transfer at a point such as a theme park. This might take more time than you are willing to spend in the morning.
If you do have a car or do not mind taking a taxi, there are a few nearby resorts. I recommend that you head to
Disney's Port Orleans Resort - French Quarter. The Sassagoula Floatworks and Food Factory there offers great breakfast options. My family stayed there recently and loved the beignets! Other nearby resorts with quick-service breakfast options include Disney's Port Orleans Resort - Riverside and Disney's Saratoga Springs Resort & Spa.
You could also head right to your destination for the day and look at the quick-service breakfast options there. For example, Sunshine Seasons at Epcot offers some great breakfast options, as does the Kusafiri Coffee Shop & Bakery at Disney's Animal Kingdom.
I hope that these thoughts are helpful for you, Tracy!