You are welcome. It wouldn't surprise me to learn that the author of that exercise book got confused and wrote "got up so early as to" by mistake, unintentionally reversing the order of the third and fourth words from a natural English expression he had seen or heard elsewhere.
And here is a bonus, free, unsolicited English lesson:
Doesn't this usage of "as to" sound natural?
What you wrote here struck me as a little odd when I first read it. A question of this form (Doesn't ...?) is usually used to convey that the speaker thinks (or suspects, or is under the impression) that the situation being asked about is TRUE, and wants confirmation.
Here are a couple of similar examples:
- Doesn't Janice look nice today? (The speaker thinks Janice looks nice.)
- Doesn't Tom currently work for Apple? (The speaker thinks or suspects or is under the impression that Tom currently works for Apple.)
In your case, though, I think that it is likely that you think / suspect that the usage of "as to" might sound
unnatural. If that is the case, then you need to word your question like this:
(e) "Doesn't this usage of "as to" sound
unnatural?"
Alternately, you could use the "Does" form, like this:
(f) "Does this usage of "as to" sound natural?"
Questions (e) and (f) are similar in meaning to each other, but (e) includes more of an implication of how the speaker feels, while (f) does not necessarily contain such an implication.
I believe that this way of forming questions is similar in Japanese -- in particular, questions which end in じゃない?