Hypothesis re babies and language

Am now regularly exposed to two children aged around one. This has just occurred to me -- I must check it out in the field (i.e. on the floor) when next I visit. It may be wrong; it may also be correct and completely familiar to those who know about this stuff.

Language, as I understand it, is known to have a different origin from animal cries. The only animal cries we human have are crying, roars of rage and such and laughing -- something like that -- I forget the formulation. These we hear from babies from the start. Only around now, though, am I beginning to notice vocal behaviour that seems the precursor of language; the nature of the distinction is my hypothesis.

Animal cries in babies are expressive, the manifestation of internal states like amusement or hunger. The sort of noises that seem to anticipate language are referential: they occur in the context of the attention being directed to something outside the self, or accompanying some operation like dropping a block into a slot. I'm not sure if these noises are getting specialised yet -- a particular vocalisation for a particular phenomenon -- in which case they would be on their way to being names.