What styles of speaking do Russian children use?

[Hugh M. Olmsted]

One place you can look for examples and general discussion, together
with some bibliography, is (despite the specialized-sounding title):

Olmsted, H.M.
Diminutive morphology of Russian children: a simplified subset of
nominal declension in language acquisition.
In:  Alexander Lipson: in memoriam (Columbus, OH: Slavica Publishers,
1994), p. 165-209.