Leigh, you seem completely confused about Dining at WDW IN GENERAL.
The
Disney Dining Plan (DDP) is relatively new, compared to how long WDW has been around (since 1971). Prior to its creation, dining at WDW was just like dining anywhere else in the world. There are restaurants. You made reservations. You pay with a credit card, cash, or charge to your room account. Same as you would do in your home town. Since the DDP has been created, you are given the OPTION to purchase it as part of a package including hotel room and tickets, pay IN ADVANCE, and recieve "credits" for meals, counter service meals, and snacks. These credits are on your hotel room key and you present that as "payment", where credits are deducted for the meal you have eaten. You are given a receipt that shows you how many of each type of CREDIT you have left. You are also free to pay for meals and snacks out of pocket, if you want to do so. By having the DDP, you are not restricted to ONLY eating what it provides. You are able to buy things at WDW with cash and credit cards same as before. Many, many people do NOT purchase the DDP, and still are able to dine in all the same establishments as those who do.
First of all, a meal plan is NOT required to dine in any of the couple HUNDRED restaurants within the WDW property. ALL the DDP is is a PREPAID meal plan. It offers a SLIGHT discount, when compared to ordering individual items a la carte. However, it is a LOT of food.
I think it is WAY too confusing for most people, especially those who are visiting WDW for the first time. There's a lot to "know" about how to use it properly, and get the most bang for your buck. Best for WDW vets, in my opinion. Also, it takes some knowledge of the WDW transportation system to avoid spending HOURS every day travelling to/from your restaurant reservations.
You also should know that WDW chefs are EXCEPTIONAL about allergies. There is a special number you can call prior to your trip to discuss your concerns for the restaurants you have made ADR for. When you arrive, they will have the chef come out and talk to you to be sure the food for your child is "safe". EVEN at buffets! They can even make special dishes that are otherwise not on the menu, in order to accommodate an allergy, so the whole family does not have to avoid a place.
My advice to you is NOT get the dining plan. Make a couple ADR's for restaurants that seem appealing to your family. Otherwise, there is a PLETHORA of places to eat "on the fly" in all the parks, resorts, and Downtown Disney. MANY of them, even if they are "counter service" provide excellent food, suitable for dinner. Trust me, everyone at WDW does not go to a sit down restaurant at dinner time! I would actually be inclined to suggest you do your sit downs at LUNCH time. Usually a lot cheaper with many of the same menus as dinner. Your 3 year old will likely be better behaved earlier in the day too! Then, for dinner, you can just eat wherever you happen to be at the time, no stress.