Check out the CHAT (Checklist for Autistic Toddlers) and skim the milestones for a 16 month old at the CDC web site, "Learn the Signs" and make sure the baby does not have any early signs of autism.
A 16 month old is eligible for Birth-to-Three services in her state, and in Michigan, ours is called "Early On". If the problem is any kind of apraxia, Nancy Kaufman at Kaufman Center in West Bloomfield, is well known for her expertise in that area.
Some parents, WITH THEIR PEDIATRICIAN'S OKAY, have used oomega 3 fatty acids with late talkers -- please research that one and don't try it w/o a doctor's okay. Check out a book called "The Late Talker," for more information.
I agree with the responder who mentioned a food allergy. And MILK (actually milk protein, called casein) would be the first thing I'd consider as a contributor. Gluten would be second. (gluten is found in grains like wheat, barley, rye, malt, and some oats, due to cross contamination issues)
I would be more concerned about the baby not being able to follow the gaze of an adult, not being able to follow the point of an adult, not being able to engage in peek-a-boo than I would worry about sounds at this point. There's a huge amount of joint attention that should have developed by 16 months, a LOT of non-verbal reciprocity that grows before labels like words come into play. Does she have a 16 month old reciprocity, non-verbally, with adults?