Which word can I use to describe random nonsense sounds like 'aaaa', 'papa' etc. from a child who still cannot speak.
According to the Facts on File Descriptionary (2000), one apt term for such sounds is lallation:
lallation any noise or utterance typical of a baby.
Merriam-Webster's Third New International Dictionary (1986) generally confirms this meaning:
lallation n 1 : infantile utterance whether in infants or in older speakers (as by retardation or mimicry) 2 : a defective articulation of the letter l, the substitution of \l\ for another sound, or the substitution of another sound for \l\—compare LAMBDACISM
Interestingly, the Oxford English Dictionary, Compact Edition (1971) asserts that the "childish utterance" meaning of lallation is obsolete, and that the only current meaning is this:
An imperfect pronunciation of r, by which the sound of that letter is confused with that of l; lambdacism.
For the record, the Third International Dictionary defines lambdacism as follows:
lambdacism n 1 : excessive use of the letter l or the sound \l\ (as in alliteration) 2 : defective articulation of \l\ or substitution of other sounds for it 3 : substitution of \l\ for another sound [example omitted] —compare LALLATION
If the baby is repeating sounds then it's echolalia.
Only tangetially related to your question I know, but I like the word.