Was she stutter by saying "do" twice, or was that for an emphasis?
No, she did not stutter here. The first "do" that she says is being used as an agreement; almost like saying "yes." The second "do" that she says is being used to indicate the action that Millie does. In this case, "do" means that Millie reads a text message and forgets to answer it. Saying "do" twice is actually fairly common in spoken English. A: You always snort like a pig when you laugh. B: I do do that! A: Why does trouble always follow you? B: I do do things that get me in trouble.