This is a very common question, so you're treading on common ground.
The short answer is no, you do not need to alter your diet or worry about carbo loading for races up to a half marathon.
Your body's natural energy stores are sufficient for a 4 miler, a 10K, or your planned October of January Disney half marathons. It won't hurt for you to be conscious of eating pastas, grains, and fruits as you lead up to the race, but you don't need to eat anything special before races like this. If you go past the half marathon distance you'll want to build your energy stores in advance through proper eating.
Another important question which you can only answer through experience is whether or not your body needs some type of light meal before a race. Many people either do not need to eat before a race or are unable to eat before a race as it upsets their stomach. My wife is one of these people. I am not one of those people, as I absolutely have to eat before a morning race, otherwise I literally fall to pieces as my body exhausts the fuel tank. After many races over many years I have found that an energy bar and a banana, washed down with a little water give my body the kick it needs in the morning, without making me feel full or sick. For Disney with the 6 a.m. start I take this down at about 4:30 and I'm ready for the beginning, middle, and end of the half marathon.
For the full I do take a few bites of the gel beginning about half way. It is truly vile stuff in my opinion, but it certainly helps.
Good luck with your races building up to Disney. The only way to find what works and doesn't work for you is to get out there, which you are doing. Good luck.
Craig