Have any ideas on foods that I should feed my 12 month old that is allergic to egg and milk products?

Many choices. In general, you should stick to a milk product that is free of milk protein, such as soy milk (silk) or almond milk. Be sure to read labels to help you avoid these foods strictly. Often, kids with minor allergies to egg can eat egg as long as it's baked in as a minor ingredient of a larger recipe. Thankfully, most children (70-80%) outgrow allergies to milk and egg protein by the age of 5.