Shouldn't "Dad" or perhaps "Daddy" be better is this situation than "Father".
Yes. Because only the younger children would ask that sort of question, don't you think so?
It is not only little children who say 'dad'
I think so too. Even though there are other alternatives to "isä" (like "isi", "iskä" and "isukki" which are not formal at all), "isä" is still completely neutral, as is "dad", when you are talking to/with your own father/dad.
When I first read this I thought they were saying their dad is a happy teddy bear.
Ah, the beauty of a language with no articles
Teddy without bear not accepted?