IMO, the most masterful development of Michael's character is that in the book.
The most important point about Michael's readiness in the book is this scene:
Tom: You are nearly as good as your father, but there's one thing you still have to learn.
Mike: What's that?
Tom: How to say no.
....
Mike to Vito: So, you've taught me everything else.

All later discussion of their plans shows that Michael's role in planning is bigger than the Don's.Don, in fact, completely retired already.
The scene DC quoted is roughly taken from book, but the intonation is changed. Mike didn't doubt his ability to be the don, his tutelage was obviously finished. He just said that he needed 4 more months to prepare and get those political connections. The suddenness of the Don's death caused him to make some changes in the original plan, as we may understand from Tom's words.