Word to describe sounds from a one-year old child
Two words are generally used to describe baby talk (the definitions are from Chambers):
- Prattle — "(of a young child) to utter baby-talk"
- Babble — "to speak like a baby"
For sounds like 'aaaa,' I would say cooing.
Sounds like 'mama,' I would say babbling.
I would probably avoid prattling because it is also used to mean annoying, incessant talking.
Babble fits your description. It can be used as a noun or verb.