One of the odd effects of playing too much adventure games is that you can start to look at the world in odd ways. For example, it now seems to me that toddlers treat the world as a text adventure. David's common approach is to go through a think-do cycle, where the 'do' is generally a simple verb-noun phrase. Moreover, it genuinely does appear to be mostly adventure-game-like: Drop ball. Look. Get book. Examine book. Give book to daddy.
I guess it makes sense. After all, they're wandering around a strange world, where they don't know the rules, trying to make sense of it all. They have a limited interface to the world (a small vocabulary, both literally, and conceptually). As with most text adventures, communications with other characters is difficult.
So, my thesis is that randomly wandering around the house, moving objects about apparently aimlessly and doing wierd things isn't actually babyish at all! If an adult were dumped in a sufficiently alien environment, they could do no better....