As you stated,
> {} or
The first one uses a colloquial contraction, but all three mean:
> "Just drink it up!"
It is perfectly natural for a child to say this to his/her father as it is a friendly kind of imperative and **not** a strict order. In nuance, it is actually close to being a friendly request rather than an "order".
Finally, the line says nothing about the size of the beer even though it is clear that there is not a whole case sitting in front of Daddy.