Hi Stacia,
Fear not, as the breakfast buffet will most definitely stay stocked whilst you enjoy your Supercalifragilistic Breakfast at
1900 Park Fare.
Likewise, the Disney Characters will continue to make their way around the restaurant, meeting and greeting guests, until such a time as they have visited all of the tables where guests are seated. Although Breakfast finishes at 11:50 AM, Dinner doesn't start until 4:00 PM so you will not be rushed at all.
I have to tell you that in my experience, having a dining reservation at a Character Meal close to the end of a specific meal time, such as breakfast, has allowed my family to spend more time with the Disney Characters as there are not as many guests for them to get around.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma