Hi, Lacey! Thanks for visiting us again here on the Disney Parks Moms Panel.
Yes, you are absolutely correct - the Disney Dining Plan includes one Quick-Service Meal, one Table-Service Meal and one Snack per person (ages 3 and up) for each night of your resort stay. The Plan also includes one Resort refillable drink mug per person for the length of your stay.
The Dining Plan would cover lunch and dinner each day, depending on the restaurants you choose (whether table service or quick service). Also, you should know that Fairytale Dining at Cinderella's Royal Table, all Signature Restaurants and the three Dinner Shows (Mickey's Backyard BBQ, Hoop-Dee-Doo Musical Revue and Disney's Spirit of Aloha Dinner Show) require two dining plan credits per person.
You would pay out-of-pocket for any additional meals or food items. Here's a tip: My family has often used our Snack credits to grab a breakfast item like a muffin, pastry or bagel in the morning (at our resort's quick-service location or in the theme parks). We usually forgo a sit-down breakfast so we can get to the parks at opening time to enjoy our favorite attractions right away. And, yes, you can always buy extra food items in the theme parks to supplement your dining plan, if necessary.
Please stop back any time with additional planning questions - I'd be happy to help!
Wishing you a magical vacation!