Is "one" necessary?
Answer from a Native speaker
We use "that one" to point to a specific object. As you can see in the clip, there are actually a variety of teddy bears that she can choose from. By saying "that one", she's being very specific about which teddy bear she wants. It is also possible to simply say "I want that" however that is generally done when you're pointing clearly at the thing you need. You could also say "I want that (thing)" so I this case, "I want that teddy". Ex: A: Which flavour ice cream do you want? B: I want that one. Ex: I think she really wanted that one. The pink one.