Is 16 too young for a chin implant?

It depends. Plastic surgeons usually want to wait until the bones have stopped growing in the face before placing a chin implant and when the patient is mature enough to know what he/she wants and participate in the recovery process. This is usually around 18 (sometimes later and sometimes earlier). There may be a compelling reason to operate earlier.
Don't overlook. Micrognathia (small jaw) can create functional as well as cosmetic problems. 16 is still a good time to address possible occlusal issues and potential jaw joint issues as well. Your 16yo would benefit from an orthodontic exam, imo to explore options now. Some of those corrections may minimize the extent or need for surgery later on and less surgery is always better.