Meatloaf made with ground beef is a good source of iron, and can be cut into small sticks that can be easily picked up with baby fingers. Another great finger food that kids love are mini muffins. You can make lots and freeze them. Use whatever recipe you like, just substitute soy milk or soy formula or juice for the milk in the recipe. Muffins are a great place to hide vegetables, liked pureed squash, or grated carrots.
Bagels are great finger, teether food.
Chunks of ripe avocados, ripe bananas, soft ripe mangos, and soft cooked apple chunks are healthy finger foods. Fun pasta shapes covered with a small amount of sauce are kid favorites. Health food stores sell many varieties of non-dairy cheese that you can use. As a matter of fact, health food stores tend to sell many things that are dairy free for their vegan customers, and milk allergy customers. Often, because they are small, their sales people are able to help you locate those items that are milk free.