Hello Tara
I am not so sure about keeping food properly frozen in most caravan fridges. Most models do have a small freezer section, but they can be temperamental in operation, and they are not as cold as your freezer at home.
I echo Parksy's suggestion of pre-cooling the fridge, and transporting a few essential frozen goods for immediate use, but then it makes sense to use the shops close to your destination.
From a slightly different perspective, if you try to take a lot of food with you, then it might surprise you how heavy it is. By only taking the essentials for say one-days provisions, you can save weight and improve the tow-ability of your caravan.