Foods which contain gluten include wheat, rye, barley and oats, all of which are important sources of iron and fibre (i.e. bread, pasta and flour for example). It is suggested to wait until your baby is at least 6 months old before you introduce gluten to your baby's diet, and at that point, you should introduce these foods with caution, as gluten is a common food allergen. Introducing it gradually will allow you watch for any signs of allergies or intolerance.
Whilst it is not recommended to cut one food group out of your diet without a good reason, foods that contain gluten are not suitable for a baby with a family history of coeliac disease or allergies. Alternative forms of iron and fibre can be introduced into your baby's diet.