Stephanie, your son can progress from using a highchair to a booster seat or a child-size table and chair any time now, depending upon his development and temperament, and what works best for you.
At 15 months, your son has graduated from infancy to toddlerhood. Typically, toddlers enjoy imitating older children and adults, trying to do things for themselves, and becoming “big boys” or “big girls.” Your son is probably feeding himself with a spoon or fork and his fingers, and drinking from a cup. Being able to sit at the family table—either in his high chair or on a booster seat strapped onto an adult-sized chair—can be a good way for him to show that he is a big boy and to encourage good eating habits. Eating with the family can help your son learn the social aspects of family meals: pleasant conversation, table manners, and eating a variety of foods. And a child-sized table with chairs can be especially good if your son has a preschool-aged sibling.
Developmentally, your son is ready for a child-size chair when he can sit in the chair in a stable and safe manner. Make sure that the chairs are low and sturdy. To sit and eat comfortably, your son’s feet should rest on the floor, and the table should come to his waist. Be sure to enforce some big-boy rules, e.g., he must sit in the chair (no standing up) and keep his feet on the floor (no rocking backwards) to prevent falls.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.