an onomatopoeic toddler

[Carol Slater]

Hi, Marie--
I don't know of any relevant studies, but if you are not already familiar with Heinz Werner's Comparative Psychology of Mental Development, you might be interested in his proposal that early symbol formation quite generally makes use of parts/aspects of the things/events symbolized and only gradually become differentiated from them. With regard to children inventing their own language, let me add to Brian McWhinney's mention of the lady from Iceland Ludwig Bemelmans's (undoubtedly apocryphal) anecdote that as a child in Austrian Tyrol his parents arranged for each of several adults to speak a different language to him, with the consequence that he did not talk until he was three, assuming that everyone had their own language and waiting patiently for his own to come along.
Do take good notes and make videotapes! 
Cheers,
Carol Slater
Psychology
Alma College
Alma MI 48801
cslater at alma.edu