Due to the rise in food allergies it is highly recommended by most Peds & Allergists to not introduce certain foods into your childs diet until the proper age.
The most common foods that can cause allergies include: peanuts, tree nuts (walnuts, pecans, etc.), fish, shellfish, eggs (especially egg whites), milk, soy, and wheat.
Infants should not be fed solid foods until they are six months old. When infants are six to 12 months old, vegetables, rice, meat, and fruit can be introduced to their diets. Each food should be introduced one at a time so parents or caregivers can identify and eliminate any foods that cause a reaction. After the child is one year old, milk, wheat, corn, citrus and soy may be added. At two years of age, the child may have egg. Finally, at age three, fish and peanuts may be introduced. Referenced from http://www.aaaai.org/
Unfortunatley their immature digestive tracts cannot filter out the allergens in these foods. It takes away some options, but it is much better to feed safely then to worry about your child going into anaphylactic shock.
Sorry this is long, but I just wanted you to be aware of what to not use as finger foods at this time!